A   SYSTEM 


OF 


GEOMETRY  AND  TRIGONOMETRY 


WITH  A 


TREATISE    ON    SURVEYING, 

IN  WHICH  THE  PRINCIPLES  OP 

RECTANGULAR   SURVEYING, 

WITHOUT    PLOTTING, 

ARE  EXPLAINED. 


BY  ABEL  FLINT,  A.M. 


STEREOTYPE    EDITION,    ENLARGED, 

WITH  ADDITIONAL  TABLES. 

BY    GEORGE    GILLET, 

SURVEYOR  GENERAL  OP  CONNECTICUT. 

HARTFORD : 

BELKNAP    AND    HAMERSLEY. 
1838. 


ENTERED, 
according  to  the  Act  of  Congress,  in  the  year  1835,  by 

EDWARD  P.  COOKE, 

in  the  Clerk's  Office  of  the  District  Court  of 
CONNECTICUT. 


v;  .-.i 


~TM 


THE  original  compiler  of  the  following  work  design- 
ed, in  preparing  it,  to  furnish  a  plain  and  concise  system 
of  PRACTICAL  SURVEYING. 

That  he  did  not  fail  of  success,  has  been  proved  by 
the  high  estimation  in  which  this  treatise  has  been,  and 
is,  at  the  present  time,  held  by  Surveyors,  and  by  the 
continued  and  increasing  demand  for  it. 

In  the  present  edition,  practical  matter, has  been  add- 
ed by  GEORGE  GILLET,  Esq.,  Surveyor  General  of  the 
state  of  Connecticut ;  and  in  addition  to  all  the  tables 
of  the  best  treatises  extant,  it  contains  the  only  table  of 
Natural  Tangents  ever  published  in  this  country. 

In  the  table  of  logarithms,  and  of  logarithmic  sines, 
&c.,  the  decimals  are  carried  to  six  figures,  and  a  co- 
lumn of  differences  is  added,  for  the  purpose  of  finding 
intermediate  numbers.  The  use  of  these  tables  is  so  fa- 
miliarly explained  and  illustrated  by  examples,  that  no 
other  instruction  upon  this  subject  is  necessary. 

The  articles  on  distributing  estates,  locating  and  sur- 
veying roads,  and  on  levelling,  cannot  fail  of  being 
highly  useful  to  the  practical  surveyor. 

The  work  being  now  used  extensively  in  schools  and 
academies,  it  has  been  the  chief  object  of  the  publishers 
to  render  it  acceptable  as  a  text  book. 


M306235 


The  subscribers  have  examined,  in  manuscript,  the  additions  to  the 
seventh  edition  of  FLINT'S  SURVEYING,  by  GEORGE  GILLET,  Esq ,  Sur- 
veyor General  of  Connecticut,  and  find  them  to  embrace  a  system  of 
correct,  useful,  and  practical  matter,  judiciously  arranged,  and  clearly 
explained  to  the  understanding  of  the  learner.  Having  long  acted  as 
Surveyors  under  public  authority,  we  recommend  this  work,  as  con- 
taining all  the  elementary  science,  and  requisite'tables,  necessary  or 
convenient  for  the  learner  and  the  practitioner.  The  present  is  a  more 
full  and  complete  system  than  any  former  edition. 

MOSES  WARREN,  Dep.  Sur.  N.  London  Co. 

LEMUEL  INGALLS,  late  Dep. Sur.  Windham  Co. 

DANIEL  ST.  JOHN,  Dep.  Sur.  Hartford  Co. 

ASAHEL  DEWEY,  County  Sur.,  N.  London  Co. 

JONATHAN  NICHOLS,  Dep.  Sur.  Windham  Co. 
Connecticut,  August,  1832. 

FLINT'S  SURVEYING  has  now  been  before  the  public  upwards  of  thirty 
years.  During  this  period,  it  has  passed  through  numerous  editions, 
and  been  enriched,  from  time  to  time,  by  important  contributions  from 
the  present  Surveyor  General,  GEORGE  GILLET,  Esq.  The  distinguish- 
ing feature  of  the  work,  as  now  published,  is  its  excellent  adaptation  to 
the  every  day  wants  of  the  practical  surveyor,  while  it  supplies  to  aca- 
demies and  private  students  an  eminently  useful,  clear,  and  well-digest- 
ed system  of  elementary  instruction,  both  in  the  theory  and  practice  of 
Surveying.  I  know  of  no  work,  in  this  respect,  which  equals  it. 

E.  H.  BURRITT,  Civil  Engineer. 

New  Britain,  Con.,  Nov.,  1835. 


GEOMETRY. 


GEOMETRY  is  a  science  which  treats  of  the  properties 
of  magnitude. 

PART    I. 
GEOMETRICAL  DEFINITIONS. 


1.  A  point  is  a  small  dot;  or,  mathematically  considered, 
is  that  which  has  no  parts,  being  of  itself  indivisible. 

2.  A  line  has  length  but  no  breadth. 

3.  A  superficies  or  surface,  called  also  area,  has  length 
nnd  breadth,  but  no  thickness.    ' 

4.  A  solid  has  length,  breadth,  and  thickness. 

5.  A  right  line  is  the  shortest  that  can  be  drawn  between 
two  points. 


6.  The  inclination  of  two  lines  meeting 
one  another,  or  the  opening  between 
them,  is  called  an  angle.  Thus,  atB,  Fig. 
1,  is  an  angle,  formed  by  the  meeting  of 
the  lines  A  B  and  B  C. 


7.  If  a  right  line  C  D,  Fig.  2,  fall  upon 
another  right  line  A  B,  so  as  to  incline  to 
neither  side,  but  make  the  angles  on  each 
side  equal,  then  those  angles  are  called 
right  angles ;  and  the  line  C  D  is  said  to  be 
perpendicular  to  the  other  line. 


Fig.  1. 


10 


GEOMETRY. 


Fig.  3. 


8.  An  obtuse  angle  is  greater  than  a 
right  angle ;  as  A  D  E,  Fig.  3. 

9.  An  acute  angle  is  less  than  a  right 
angle;  asEDB,  Fie.  3. 


NOTE.  When  three  letter?  arc  used  to  express  an  angle, 
the  middle  letter  denotes  the  angular  point. 

10.  A  circle  is  a  round  figure  bounded         Fig.  4. 
by  a  single  line,  in  every  part  equally  dis-  ^ 

tant  from  some  point,  which  is  called  the        ^ \ 

centre.     Fig.  4.  /  \ 

11.  The  circumference  or  periphery  of  a  -J £     \ 

circle   is   the  bounding  line ;  as  A  D  E  B,      * 

Fig.  4. 

12.  The  radius   of   a    circle   is   a    line 
drawn  from   the    centre    to  the    circumfe- 
rence ;  as  C  B,  Fig.  4.     Therefore  all  radii 
of  the  same  circle  are  equal. 

13.  The  diameter  of  a  circle  is  a  right 
'line  drawn  from  one  side  of  the  circumfe- 
rence to  the  other,  passing  through  the  cen- 
tre ;  and  it  divides  the  circle  into  two  equal 
parts,  called  semicircles;  as  ABor   DE, 
Fig.  5. 

14.  The  circumference  of  every  circle 
is  supposed  to  be  divided  into  360  equal 
parts,  called  degrees  ;  and  each  degree  into 
60  equal  parts,   called  minutes;  and  each 
minute  into  60  equal  parts,  called  seconds  ; 
and  these  into  thirds,  &c. 

NOTE.  Since  all  circles  are  divided  into  the  same  num- 
ber of  degrees,  a  degree  is  not  to  be  accounted  a  quan- 
tity of  any  determinate  length,  as  so  many  inches  or  feet, 
&c.  but  is  always  to  be  reckoned  as  being  the  360th  part 
of  the  circumference  of  any  circle,  without  regarding  the 
size  of  the  circle. 

15.  An  arc  of  a  circle  is  any  part  of  the  circumference; 
as  B  F  or  F  D,  Fig.  5  ;  and  is  said  to  be  an  arc  of  as  many 
degrees  as  it  contains  360th  parts  of  the  whole  circle. 


Fig.  5. 


GEOMETRY. 


11 


16.  A  chord  is  a  right  line  drawn  from 
one  end  of  an  arc  to    another,  and  is  the 
measure  of  the  arc ;  as  H  G  is  the  chord  of  A 
the  arc  H  I  G,  Fig.  6. 


NOTE.  The  chord  of  an  arc  of  60  degrees  is  equal  in 
length  to  the  radius  of  the  circle  of  which  the  arc  is  a 
part. 

17.  The  segment  of  a  circle  is  a  part  of  a  circle  cut  off 
by  a  chord;  thus,  the  space  comprehended  between  the  arc 
H  I  G  and  the  chord  H  G  is  called  a  segment.  Fig.  6. 

18.  A  sector  of  a  circle  is  a  space  contained  between  two 
radii,  and  an  arc  less  than  a  semicircle ;  as  B  C  D,  or  A  C  D, 
Fig.  6. 


19.  The  sine  of  an  arc  is  a  line  drawn  Fig.  7. 
from  one   end   of  the   arc,  perpendicular 

to  the  radius  or  diameter  drawn  through 
the  other  end  :  or,  it  is  half  the  chord  of 
double  the  arc ;  thus,  H  L  is  the  sine  of 
the  arc  H  B,  Fig.  7. 

20.  The  sines  on  the  same  diameter  in- 
crease in  length  till  they  come  to  the  cen-A 
tre,  and  so  become  the  radius,  after  whjch 
they  diminish.     Hence  it  is  plain  that  the 
sine  of  90  degrees  is  the  greatest  possible 
sine,  and  is  equal  to  the  radius. 

21.  The  versed  sine  of  an  arc  is  that  part  of  the  diameter 
or  radius  which  is  between  the  sine  and  the  circumference; 
thus  L  B  is  the  versed  sine  of  the  arc  H  B,   Fig.  7. 

22.  The  tangent  of  an  arc  is  a  right  line  touching  the 
circumference,  and  drawn  perpendicular  to  the  diameter ;  and 
is  terminated  by  a  line  drawn  from  the  centre  through  the 
other  end  of  the  arc ;  thus,  B  K  is  the  tangent  of  the  arc  B  H, 
Fig.  7. 

NOTE.  ,  The  tangent  of  an  arc  of  45  degrees  is  equal  in 
length  to  the  radius  of  the  circle  of  which  the  arc  is  a 
part. 


12  GEOMETRY. 

23.  The  secant  of  an  arc  is  a  line  drawn  from  the  centre 
through  one  end  of  the  arc  till  it  meets  the  tangent;  thus, 
C  K  is  the  secant  of  the  arc  B  H,  Fig.  7. 

24.  The  complement  of  an  arc  is  what  the  arc  wants  of  90 
degrees,  or  a  quadrant:  thus,  H  D  is  the  complement  of  the 
arc  B  H,  Fig.  7. 

25.  The  supplement  of  an  arc  is  what  the  arc  wants  of  180 
degrees,  or  a  semicircle ;  thus  A  D  H  is  the  supplement  of  the 
arc  B  H,  Fig.  7. 

NOTE.  It  will  be  seen  by  reference  to  Fig.  7,  that  the  sine 
of  any  arc  is  the  same  as  that  of  its  supplement.  So, 
likewise,  the  tangent  and  secant  of  any  arc  are  used 
also  for  its  supplement. 

26.  The  sine,  tangent,  or  secant,  of  the  complement  of  any 
arc,  is  called  the  co-sine,  co-tangent,  or  co-secant  of  the  arc ; 
thus,  F  H  is  the  sine,  D  I  the  tangent,  and  C  I  the  secant  of  the 
arc  D  H ;  or  they  are  the  co-sine,  co-tangent,  and  co-secant 
of  the  arc  B  H,  Fig.  7. 

[The  terms  sine,  tangent,  and  secant,  are  abbreviated  thus  : 
sin.,  tan.,  and  sec.  So,  likewise,  co-sine,  co-tangent,  and  co- 
secant, are  written  co-sin.,  co-tan.,  and  co-sec.] 

27.  The  measure  of  an  angle  is  the  arc  of  a  circle  contain- 
ed between  the  two  lines  which  form  the  angle,  the  angular 
point  being  the  centre ;  thus,  the  angle  H  C  B,  Fig.  «7,  is  mea- 
sured by  the  arc  B  H  ;  and  is  said  to  contain  as  many  degrees 
as  the  arc  does. 

NOTE.  An  angle  is  esteemed  greater  or  less,  according  to 
the  opening  of  the  lines  which  form  it,  or  as  the  arc  in- 
tercepted  by  those  lines  contains  more  or  fewer  degrees. 
Hence  it  may  be  observed,  that  the  size  of  an  angle  does 
not  depend  at  all  upon  the  length  of  the  including  lines; 
for  all  arcs  described  on  the  same  point,  and  intercepted 
by  the  same  right  lines,  contain  exactly  the  same  num- 
ber of  degrees,  whether  the  radius  be  longer  or  shorter. 

28.  The  sine,  tangent,  or  secant  of  an  arc,  is  also  the  sine, 
tangent,  or  secant  of  the  angle  whose  measure  the  arc  is. 

Fig.  8. 

29.  Parallel  lines  are  such  as  are  equal-  ^ -g 

ly  distant  from  each  other ;  as  A  B  and  C  D, 

* 8- 


GEOMETRY. 


13 


30.  A  triangle  is  a  figure  bounded  by 
three  lines ;  as  A  B  C,  Fig.  9. 

31.  An  equilateral  triangle  has  its  three 
sides  equal  in  length  to  each  other.  Fig.  9. 


32.  An  isosceles  triangle  has  two  of  its  sides 
equal.     Fig.  10. 


fig.  10. 


Fig.  11. 


33.  A  scalene  triangle  has  three  unequal        / 
sides.     Fig.  11.  / 


Fig.  12. 


34.  A  right  angled  triangle  has  one 
right  angle.     Fig.  12. 


35.  An  obtuse  angled  triangle  has  one 
obtuse  angle.     Fig.  13. 


36.  An  acute  angled  triangle  has  all   its   angles  acute. 
Fig.  9,  or  10. 

37.  Acute  and  obtuse  angled  triangles,  are  called  oblique 
angled  triangles,  or  simply  oblique  triangles ;  in  which  the 
lower  side  is  generally  called  the  base,  and  the  other  two, 
legs. 

38.  In  a  right  angled  triangle,  the  longest  side  is  called  the 
hypothenuge,  and  the  other  two,  legs,  or  base,  and  perpen- 
dicular. 

2* 


14 


GEOMETRY. 


NOTE.  The  three  angles  of  every  triangle  being  added 
together  will,  amount  to  180  degrees;  consequently  the 
two  acute  angles  of  a  right  angled  triangle  amount  to  90 
degrees,  the  right  angle  being  also  90. 


39.  The  perpendicular  height  of  a  tri- 
angle is  a  line  drawn  from  one  of  the  angles 
perpendicular  to  its  opposite  side  ;  thus,  the 
dotted  line  A  D,  Fig.  14,  is  the  perpen- 
dicular height  of  the  triangle  ABC. 


NOTE.  This  perpendicular  may  be  drawn  from  either  of 
the  angles ;  and  whether  it  falls  within  the  triangle,  or 
on  one  of  the  lines  continued  beyond  the  triangle,  is 
immaterial. 


Fig.  15. 


40.  A  square  is  a  figure  bounded  by  four 
equal  sides,  and  containing  four  right  angles. 
Fig.  15. 


41.  A  parallelogram,  or  oblong  square, 
is  a  figure  bounded  by  four  sides,  the  oppo- 
site ones  being  equal,  and  the  angles  right.* 
Fig.  16. 


42.  A  rhombus  is  a  figure  bounded  by 
four  equal  sides,  but  has  its  angles  oblique. 
Fig.  17. 


Fig.  16. 


Fig.  17. 


*  Any  four  sided  figure,  having  its  opposite  sides  parallel,  is  a  pa- 
rallelogram ;  but,  in  this  book,  the  term  is  understood  as  it  is  here  ex- 
plained. Sometimes  this  figure  is  called  a  rectangle. 


GEOMETRY.  15 

Fig.  18. 

A 

43.  A  rhomboid  is  a  figure  bounded 
by  four  sides,  the  opposite  ones  being 
equal,  but  the  angles  oblique.  Fig.  18. 


44.  The  perpendicular  height  of  a  rhombus  or  rhomboi- 
des,  is  a  line  drawn  from  one  of  the  angles  to  its  opposite 
side;  thus,  the  dotted  lines  A  B,  Figs.  17  and  18,  represent 
the  perpendicular  heights  of  those  figures. 

Fig.  19. 


r 


45.  A  trapezoid  is  a  figure  bounded  by 
four  sides,  two  of  which  are  parallel,  though 
of  unequal  lengths.  Fig.  19  and  Fig,  20. 


\ 


Fig.  20. 

NOTE.     Fig.  19  is  sometimes  called  a  right  angled  trape- 
zium. 

Fig.  21. 

46.  A  trapezium  is  a  figure  bounded  by 
four  unequal  sides.     Fig.  21. 

47.  A  diagonal  is  a  line  drawn  between 
two  opposite  angles  ;  as  the  line  A  B,  Fig 
21. 


48.  Figures  which  consist  of  more  than-  four  sides  are 
called  polygons ;  if  the  sides  are  equal  to  each  other,  they  are 
called  regular  polygons,  and  are  sometimes  named  from  the 
number  of  their  sides,  as  pentagon,  or  hexagon,  a  figure  of  five 
or  six  sides,  &c. ;  if  the  sides  are  unequal,  they  are  called 
irregular  polygons. 


16  GEOMETRY. 


PART   II. 
GEOMETRICAL  PROBLEMS. 

Fig.  22, 

PROBLEM  I.    To  draw  a  line  paral-       C          D 
lei  to  another  line  at  any  given  distance  ; 
as  at  the  point  D,  to  make  a  line  parallel     _  •>•  ____  .,..-' 
to  the  line  A  B.     Fig.  22.  AE 

With  the  dividers  take  the  nearest  distance  between  the 
point  D  and  the  given  line  A  B  ;  with  that  distance  set  one 
foot  of  the  dividers  any  where  on  the  line  A  B,  as  at  E,  and 
draw  the  arc  C  ;  through  the  point  D  draw  a  line  so  as  just  to 
touch  the  top  of  the  arc  C. 

A  more  convenient  way  to  draw  parallel  lines  is  with  a 
parallel  rule.  [The  parallel,  rules,  however,  found  in  cases 
of  mathematical  instruments,  are  often  inaccurate.] 

Fig.  23. 


PROBLEM    II.      To  bisect  a  given 
line  ;  or,  to  find  the  middle  of  it.    Fig.  23. 


D 


Open  the  dividers  to  any  convenient  distance,  more  than 
half  the  given  line  A  B,  and  with  one  foot  in  A,  describe  an 
arc  above  and  below  the  line,  as  at  C  and  D ;  with  the  same 
distance,  and  one  foot  in  B,  describe  arcs  to  cross  the  former ; 
lay  a  rule  from  C  to  D,  and  where  the  rule  crosses  the  line, 
as  at  E,  will  be  the  middle. 

Fig.  24. 
H 

PROBLEM  III.      To  erect  a  perpen-  ^ 

dicular  from   the  end,  or  any  part  of  a  ..•-"" 

given  line.     Fig.  24.  / 


GEOMETRY. 


17 


Open  the  dividers  to  any  convenient  distance,  as  from  D 
to  A,  and  with  one  foot  on  the  point  D,  from  which  the  per- 
pendicular is  to  be  erected,  describe  an  arc,  as  A  E  G ;  set  off 
the  same  distance  A  D,  from  A  to  E,  and  from  E  to  G ;  upon 
E  and  G  describe  two  arcs  to  intersect  each  other  at  H ; 
draw  a  Hne  from  H  to  D,  and  one  line  will  be  perpendicular 
to  the  other. 

NOTE.    There  are  other  methods  of  erecting1  a  perpendicu- 
lar, but  this  is  the  most  simple. 

Fig.  25. 


PROBLEM  IV.  From  a  given 
point,  as  at  C,  to  drop  a  perpendicular 
on  a  given  line  A  B,  Fig.  25. 


*    Gr 


With  one  foot  of  the  dividers  in  C,  describe  an  arc  to  cut 
the  given  line  in  two  places,  as  at  F  and  G  ;  upon  F  and  G 
describe  two  arcs  to  intersect  each  other  below  the  line,  as 
at  D;  lay  a  rule  from  C  to  D,  and  draw  a  line  from  C  to  the 
given  line. 

Perpendiculars  may  be  more  readily  raised  and  let  fall,  by 
a  small  square  made  of  brass,  ivory,  or  wood. 

Fig.  26. 


PROBLEM  V.    To  make  an  angle  af£, 
equal  to  a  given  angle  ABC,  Fig.  26.  " 


Open  the  dividers  to  any  convenient  distance,  and  with 
one  foot  in  B,  describe  the  arc  F  G ;  with  the  same  distance, 
and  one  foot  in  E,  describe  an  arc  from  H ;  measure  the  arc 
F  G,  and  lay  off  the  same  distance  on  the  arc  from  H  to  I ; 
draw  a  line  through  I  to  E,  and  the  angles  will  be  equal. 

Fig.  27. 

PROBLEM  VI.  To  make  an  acute  an- 
gle equal  to  a  given  number  of  degrees,  sup- 
pose 36.  Fig.  27. 


18  GEOMETRY. 

Draw  the  line  A  B  of  any  convenient  length ;  from  a  scale 
of  chords  take  60  degrees  with  the  dividers,  and  with  one 
foot  in  B,  describe  an  arc  from  the  line  A  B  5  from  the  same 
scale  take  the  given  number  of  degrees,  36,  and  lay  it  on  the 
arc  from  C  to  D;  draw  a  line  from  B  through  D,  and  the 
angle  at  B  will  be  an  angle  of  36  degrees. 

28. 


PROBLEM  VII.  x  To  make  an  obtuse 
angle,  suppose  of  110  degrees.  Fig.  28. 


B 

Take  a  chord  of  60  degrees  as  before,  and  describe  an  arc 
greater  than  a  quadrant ;  set  oft'  90  degrees  from  B  to  C,  and 
from  C  to  E  set  off  the  excess  above  90,  which  is  20 ;  draw 
a  line  from  G  through  E,  and  the  angle  will  contain  110  de- 
grees. 

[It  is  best,  however,  in  making  obtuse  angles,  to  take  from 
the  scale  the  chord  of  half  the  angle,  and  set  it  off  twice. 
This  will  save  taking  two  separate  chords.] 

NOTE.  In  a  similar  manner  angles  may  be  measured  ;  that 
is,  with  a  chord  of  60  degrees  describe  an  arc  on  the 
angular  point,  and  on  a  scale  of  chords  measure  the  arc 
intercepted  by  the  lines  forming  the  angle. 

A  more  convenient  method  of  making  and  measuring  an- 
gles, is  to  use  a  protractor  instead  of  a  scale  and  dividers. 


Fig.  29. 
O 


B 

PROBLEM  VIII.  To  make  a  trianglej, 
of  three  given  lines,  as  B  O,  B  L,  L  O,  Fig. 
29,  any  two  of  which  are,  greater  than  the, 
third. 


Draw  the  line  B  L  from  B  to  L ;  from  B,  with  the  length 
of  the  line  B  O,  describe  an  arc  as  at  O ;  from  L,  with  the 
length  of  the  line  L  O,  describe  another  arc,  to  intersect  the 
former ;  from  O  draw  the  lines  O  B  and  O  L,  and  B  0  L  will 
be  the  triangle  required. 


GEOMETRY.  19 

Fig.  30. 


PROBLEM  IX.  To  make  a  right  an- 
gled triangle,  the  hypothenuse  and  angles 
being  given.  Fig.  30. 

Suppose  the  hypothenuse  C  A  25  rods  or  chains,  the  an- 
gle at  C  35°  30',  and  consequently  the  angle  at  A  54°  30'. 

See  note  after  the  38th  Geometrical  Definition. 

NOTE.  When  degrees  and  minutes  are  expressed,  they  are 
distinguished  from  each  other  by  a  small  cipher  at  the 
right  hand  of  the  degrees,  and  a  dash  at  the  right  hand 
of  the  minutes ;  thus,  35°  30',  is  35  degrees  and  30  mi- 
nutes. 

Draw  the  line  C  B  an  indefinite  length ;  at  C  make  an  angle 
35°  30';  through  where  that  number  of  degrees  cuts  the  arc, 
draw  the  line  C  A  25  rods,  which  must  be  taken  from  some 
scale  of  equal  parts;  drop  a  perpendicular  from  A  to  B,  and 
the  triangle  will  be  completed. 

[A  scale  of  equal  parts  may  be  found  on  one  side  of  Gun- 
ter's  scale,  occupying  half  its  length.  It  will  be  known  by 
slanting  lines  which  cross  it  at  each  end.  The  length  of  the 
scale,  not  occupied  by  these  oblique  lines,  is  equally  divided 
into  several  larger  divisions,  numbered  on  one  side,  and  like- 
wise twice  as  many  smaller,  numbered  on  the  other.  In  ta- 
king distances  from  the  scale,  each  of  these  divisions,  (either 
the  larger  or  the  smaller,  as  is  most  convenient,)  must  be 
considered  1,  10,  100,  &c.  rods,  chains,  or  other  dimensions 
of  length.  If  each  division  be  called  1,  it  will  be  easy  to 
take  off  the  required  number.  But  the  scale  is  not  usually 
long  enough  for  this.  When  each  division  is  called  10,  as 
many  divisions  must  be  taken,  as  there  are  tens  in  the  given 
number.  For  the  excess  of  tens,  in  this  case,  the  little  scale 
with  the  oblique  lines  is  used.  Each  side  of  this  little  scale 
is  divided  into  10  equal  parts,  and  each  of  these  parts  is,  of 
course,  1.  Then  to  take  off  the  hypothenuse,  25,  above,  we 
should  take  in  the  dividers  2  of  the  divisions  of  the  large 
scale,  and  5  of  those  of  the  small  one.  There  is  one  of  these 
little  scales  for  the  greater,  and  one  for  the  smaller  divisions 
of  the  large  scale.  When  each  division  of  the  large  scale 
is  called  100^  each  of  those  of  the  small  one  becomes  10,  and 
the  units  are  found  by  means  of  the  oblique  lines.  These 


20  GEOMETRY. 

are  drawn  across  parallel  lines,  running  the  whole  length  of 
the  scale,  from  each  division  on  one  side,  to  the  next  higher 
on  the  other.  The  parallel  lines  divide  the  width  of  the 
scale  into  10  equal  parts.  Since  each  oblique  line,  then,  in 
crossing  the  scale,  passes  over  one  division  of  length,  it  is 
evident  that,  in  passing  one  tenth  across,  (that  is  to  the 
first  parallel  line,)  it  will  pass  over  one  tenth  of  a -division  of 
length;  in  passing  two  tenths  across,  (  that  is,  to  the  second 
parallel  line,)  it  will  pass  over  two  tenths  of  a  division  of 
length,  and  so  on.  The  parallel  lines  are  numbered  at  the 
end  of  the  scale.  To  take  off  a  distance,  containing  hun- 
dreds, then,  as  234,  we  must  place  one  foot  of  the  dividers 
on  the  second  division  of  the  larger  scale,  and  on  the  paral- 
lel line  marked  4,  and  extend  the  other  foot  to  the  third  ob- 
lique line.  Decimals  may  evidently  be  taken  off  in  a  simi- 
lar manner ;  the  divisions  of  the  larger  scale  being  made 
units,  and  those  of  the  smaller,  tenths  and  hundredths.} 

NOTE.  The  length  of  the  two  legs  may  be  found  by  mea- 
suring them  upon  the  same  scale  of  equal  parts  from 
which  the  hypothenuse  was  taken. 

Kg.  31. 

TJ 

PROBLEM  X     To  make  a  right 
angled  triangle,  the  angles  and  one 
being  given.  Fig.  31. 


285 

Suppose  the  angle  at  C  33°  15',  and  the  leg  A  C  285. 

Draw  the  leg  A  C,  making  it  in  length  285  ;  at  A  erect  a 
perpendicular  an  indefinite  length;  at  C  make  an  angle  of 
33°  15' ;  through  where  that  number  of  degrees  cuts  the  arc, 
draw  a  line  till  it  meets  the  perpendicular  at  B. 

NOTE.  If  the  given  line  C  A  should  not  be  so  long  as  the 
chord  of  60°,  it  may  be  continued  beyond  A,  for  the  pur- 
pose of  making  the  angle. 

Fig.  32. 


PROBLEM  XL  To  make  a  right  an- 
gled triangle,  the  hypothenuse  and  one  leg 
being  given.  Fig.  32. 


GEOMETRY. 


Suppose  the  hypothenuse  A  C  40,  and  the  leg-  A  B  28. 

Draw  the  leg  A  B  in  length  28;  from  B  erect  a  perpen- 
dicular an  indefinite  length;  take  40  in  the  dividers,  and  set- 
ting one  foot  in  A,  wherever  the  other  foot  strikes  the  perpen- 
dicular will  be  the  point  C. 

NOTE.  When  the  triangle  is  constructed,  the  angles  may 
be  measured  by  a  protractor,  or  by  a  scale  of  chords. 

Fig.  33. 


PROBLEM  XII.  To  make  a  right 
angled  triangle,  the  two  legs  being  given. 
Fig.  33. 


B 


Suppose  the  leg  A  B  38,  and  the  leg  B  C  46. 
Draw  the  leg  A  B  in  length  38 ;  from  B  erect  a  perpen- 
dicular to  C,  in  length  46 ;  and  draw  a  line  from  A  to  C. 


Fig.  34. 


PROBLEM  XIII.    To 

make  an  oblique  angled  tri- 
angle, the  .  angles  and  one 
side  being  given.  Fig.  34. 


Suppose  the  side  B  C  98;  the  angle  at  B  45°  15',  the  an- 
gle at  D  108°  30',  consequently  the  other  angle  26°  15'. 

Draw  the  side  B  C  in  length  98 ;  on  the  point  B  make 
an  angle  of  45°  15' ;  on  the  point  C  make  an  angle  of  26° 
1 5',  and  draw  the  lines  B  D  and  C  D. 

Fig.  35. 

PROBLEM  XIV.  To  make  an  ob- 
lique angled  triangle,  two  sides  and  an 
angle  opposite  to  one  of  them  being  given. 
Fig.  35.  B 

Suppose  the  side  B  C  160,  the  side  B  D  79,  and  the  angle 
at  C  29°  9'. 

3 


GEOMETRY. 


Draw  the  side  B  C  in  length  160 ;  at  C  make  an  angle  of 
29°  9',  and  draw  an  indefinite  line  through  where  the  degrees 
cut  the  arc ;  take  79  in  the  dividers,  and  with  one  foot  in  B 
lay  the  other  on  the  line  CD;  the  point  D  will  be  the  other 
angle  of  the  triangle. 

Fig.  36. 

PROBLEM  XV.      To  make  an  » 

oblique  angled  triangle,  two  sides 
and  their  contained  angle  being 
given.  Fig.  36. 


Suppose  the  side  B  C  109,  the  side  B  D  76,  and  the  angle 
atB  101°  30'. 

Draw  the  side  B  C  in  length  109  ;  at  B  make  an  angle  of 
101°  30',  and  draw  the  side  B  D  in  length  76;  draw  a  line 
from  D  to  C,  and  it  is  done. 


Fig.  37. 


PROBLEM  XVI. 

Fig.  37. 


To  make  a  square. 


Draw  the  line  A  B  the  length  of  the  proposed  square ; 
from  B  erect  a  perpendicular  to  C,  and  make  it  of  the  same 
length  as  A  B ;  from  A  and  C,  with  the  same  distance  in  the 
dividers,  describe  arcs  intersecting  each  other  at  D,  and  draw 
the  lines  A  D  and  D  C. 

Fig.  38. 
D € 


PROBLEM  XVII. 

tangle.     Fig.  38. 


To  make  a  rec- 


Draw  the  line  A  B  equal  to  the  longest  side  of  the  rectan- 
gle ;  on  B  erect  a  perpendicular  the  length  of  the  shortest  side 
to  C ;  from  C,  with  the  longest  side,  and  from  A,  with  the 
shortest  side,  describe  arcs  intersecting  each  other  at  D,  and 
draw  the  lines  A  D  and  C  D. 


GEOMETRY. 


PROBLEM  XVIII.  To  de- 
scribe a  circle  which  shall  pass 
through  any  three  given  points, 
not  lying  in  a  right  line,  as  A, 
B,  D.  Fig.  39: 


Draw  lines  from  A  to  B,  an.d  from  B  to  D ;  bisect  those 
lines  by  PROBLEM  II,  and  the  point  where  the  bisecting  lines 
intersect  each  other,  as  at  C,  will  be  the  centre  of  the  circle. 

PROBLEM  XIX.      To  find  the  centre  of  a  circle. 

By  the  last  PROBLEM  it  is  plain,  that  if  three  points  be  any 
where  taken  in  the  given  circle's  periphery,  the  centre  of  the 
circle  may  be  found  as  there  taught. 

Directions  for  constructing  irregular  figures  of  four  or 
more  sides,  may  be  found  in  the  following  treatise  on  SUR- 
VEYING, 


TRIGONOMETRY. 


TRIGONOMETRY  is  that  part  of  practical  GEOMETRY, 
by  which  the  sides  and  angles  of  triangles .  are  measured ; 
whereby  three  things  being  given,  either  all  sides,  or  sides  and 
angles,  a  fourth  may  be  found ;  either  by  measuring  with  a 
scale  and  dividers,  according  to  the  PROBLEMS  IN  GEOME- 
TRY, or  more  accurately  by  calculation  with  logarithms,  or 
with  natural  sines. 

TRIGONOMETRY  is  divided  into  two  parts,  rectangular  and 
oblique-angular. 

PART  I. 
RECTANGULAR  TRIGONOMETRY. 

This  is  founded  on  the  following  methods  of  applying  a 
circle  to  a  triangle. 

Fig.  40. 

PROPOSITION  I.  In  every  right 
angled  triangle,  as  A  B  C,  Fig.  40,  it 
is  plain  from  Fig.  7,  compared  with 
the  Geometrical  definitions  to  which 
that  Figure  refers,  that  if  the  hypothe-  A, 
nuse  A  C  be  made  radius,  and  with  it  \ 
an  arc  of  a  circle  be  described  from  each 
end,  B  C  will  be  the  sine  of  the  angle 
at  A,  and  A  B  the  sine  of  the  angle  at 
C;  that  is,  the  legs  will  be  sines  of 
their  opposite  angles. 


— i. 


PROPOSITION  II.  If  one  leg,  A  B, 
Fig.  41,  be  made  radius,  and  with  it  on 
the  point  A  an  arc  be  described,  then 
B  C,  the  other  leg,  will  be  the  tangent, 
and  A  C  the  secant  of  the  angle  at  A ; 
and  if  B  C  be  made  radius,  and  an  arc 
be  described  with  it  on  the  point  C,  then 
A  B  will  be  the  tangent,  and  A  C  the  se- 
cant of  the  angle  at  C ;  that  is,  if  one 


Fig.  41. 


GEOMETRY.  25 

leg  be  made  radius,  the  other  leg  will  be  a  tangent  of  its  op- 
posite angle,  and  the  hypothenuse  a  secant  of  the  same  an- 
gle. 

Thus,  as  different  sides  are  made  radius,  the  other  sides 
acquire  different  names,  \Vhich  are  either  sines,  tangents,  or 
secants. 

As  the  sides  and  angles  of  triangles  bear  a  certain  propor- 
tion to  each  other,  two  sides  and  one  angle,  or  one  side  and 
two  angles  being  given,  the  other  sides  or  angles  may  be 
found  by  instituting  proportions,  according  to  the  following 
rules. 

—  « 

RULE  I.  To  find  a  side,  either  of  the  sides  may  be  made 
radius,  then  institute  the  following  proportion: 

As  THE  NAME  OF  THE  SIDE  GIVEN,  (which  will  be  either 
radius,  sine,  tangent,  or  secant;) 

Is  TO  THE  LENGTH  OF  THE  SIDE  GIVEN  ; 

So  IS  THE  NAME  OF  THE  SIDE  REQUIRED,  (which  also  will 

be  either  radius,  sine,  tangent,  or  secant ;) 

To  THE  LENGTH  OF  THE  SIDE  REQUIRED. 

RULE  II.  To  find  an  angle,  one  of  the  given  sides  must 
be  made  radius,  then  institute  the  following  proportion  : 

AS   THE   LENGTH   OF  THE   GIVEN   SIDE   MADE  RADIUS  j 

Is  TO  ITS  NAME,  (that  is,  radius ;) 

So  IS  THE   LENGTH  OF  THE  OTHER  GIVEN  SIDE  } 

To  ITS  NAME,  (which  will  be  either  sine,  tangent,  or  se- 
cant.) 

Having  instituted  the  proportion,  look  for  the  correspond- 
ing logarithms,  in  the  logarithms  of  numbers  for  the  length 
of  the  sides  ;  and  in  the  table  of  artificial  sines  and  tangents, 
for  the  logarithmic  sine,  tangent,  or  secant. 

ADD  TOGETHER  THE  LOGARITHMS  OF  THE  SECOND  AND 
THIRD  TERMS,  AND  FROM  THEIR  SUM  SUBSTRACT  THE  LOGA- 
RITHM OF  THE  FIRST  TERM  .*  THE  REMAINDER  WILL  BE  THE 
LOGARITHM  OF  THE  FOURTH  TERM,  WHICH  SEEK  IN  THE  TA- 
BLES, AND  FIND  ITS  CORRESPONDING  NUMBER,  OR  DEGREES 
AND  MINUTES. 

See  the  introduction  to  the  table  of  logarithms ;  which 
should  be  attentively  studied  by  the  learner,  before  he  pro- 
ceeds any  further. 

NOTE.  The  logarithm  for  radius  is  always  10,  which  is 
the  logarithmic  sine  of  90°,  and  the  logarithmic  tangent 
of  45. 


26  GEOMETRT, 

The  preceding  PROPOSITIONS  and  RULES  being  duly  at- 
tended to,  .the  solution  of  the  following  CASES  of  Rectangu- 
lar Trigonometry  will  be  easy.* 


CASE    I. 


The  angles  and  hypothenuse  given,  to 
find  the,  legs.  Fig.  42. 

A- 

In  the  triangle  AB  C,  given  the  hypothenuse  A  C  25  rods 
or  chains;  the  angle  at  A  35°  30':  and  consequently  the 
angle  at  C  54°  30':  (See  Note,  GEOM.  Def.  38.)  to  find  the 
legs. 

Making  the  hypothenuse  radius,  the  proportions  will  be : 


To  find  the  leg  A  B. 

As  radius          10.000000 

:  hyp.  AC,  25       -     1.397940 
:  :  sine  ACB,  54°  30' 9.9 10686 


11.308626 
10.000000 


To  find  the  leg  E  C. 
As  radius  -  -  -  10.000000 
:  hyp.  AC,  25  -  1.397940 
:  :  sineCAB,  35°30'  9.763954 


11.161894 
10.000000 


:  leg  AB,  20. 35  nearly  1.308626  :legBC,  14.52  nearly  1. 161894 


NOTE.  When  the  first  term  is  radius,  it  may  be  substract- 
ed  by  cancelling  the  first  figure  of  the  sum  of  the  other 
two  terms. 

As  secants  are  excluded  from  the  tables,  such  cases  in 
Trigonometry  as  are  solved  by  secants  are  also  excluded. 

[The  learner  should  exercise  himself,  in  this  and  the  fol- 
lowing rules  in  TRIGONOMETRY,  in  stating  all  the  propor- 
tions which  can  be  made,  until  he  is  able  to  do  it  with  fa- 
cility.] - 

*  See  Practical  Trigonometry  in,  the  Appendix. 


TRIGONOMETRY.  27 

BY  NATURAL  SINES. 

This  CASE  may  be  solved  by  natural  sines,*  according  to 
the  following  proportions  : 

As  UNITY,  OR  1,  IS  TO  THE  LENGTH  OF  THE  HYPOTHENUSE, 
SO  IS  THE  NATURAL  SINE  OF  THE  SMALLEST  ANGLE,  TO  THE 
LENGTH  OF  THE  SHORTEST  LEG.  OR,  SO  IS  THE  NATURAL 
SINE  OF  THE  LARGEST  ANGLE,  TO  THE  LENGTH  OF  THE  LONG- 
EST LEG. 

Or,  which  is  the  same  thing,   MULTIPLY  THE  NATURAL 

SINES    OF  THE  TWO    ANGLES    BY  THE  HYPOTHENUSE  J    THE 
PRODUCTS  WILL  BE  THE  LENGTH  OF  THE  TWO  LEGS. 

EXAMPLE. 

Nat.  sine  of  35°  30'      Nat.  sine  of  54°  30' 

0.58070  0.81412 

Hyp.       25   „      Hyp.      25 


290350  407060 

116140  162824 


14.51750  20.35300 


LegBC   14.52         Leg  AB  20.35 

NOTE.  The  third  decimal  figure  in  the  first  product  be- 
ing 7,  the  preceding  figure  may  be  called  one  more  than 
it  is,  viz.  2.  And  whenever  in  any  product,  &c.  there 
are  more  places  of  decimals  than  you  wish  to  work 
with,  if  the  one  at  the  right  hand  of  the  last  which  you 
wish  to  retain  is  more  than  5,  add  a  unit  to  the  last,  be- 
cause a  greater  decimal  number  than  5  is  more  than  half. 


CASE    II. 


The  angles  and  one  leg  given,  to  find  the 
hypothenuse  and  the  other  leg.  Fig.  43. 

B 


*  See  the  Introduction  to  the  Table  of  Natural  Sines. 


28  TRIGONOMETRY. 

In  the  triangle  ABC,  given  the  leg  A  B  325,  the  angle  at 
A  33°  15',  and  the  angle  at  C  56°  45';  to  find  the  hypothe- 
nuseand  the  leg  BC. 

Making  the  hypothenuse  radius,  the  proportions  will  be ; 


To  find  the.  hypothenuse. 
As  sine  of  C,  56°  45'  9.922355 
:leg  AB,  325.  2.511883 


To  find  the  leg  BC. 
As  sine  of  C,  56°  45'  9.922355 
:  leg-  AB,   325          2.511883 


Radius  10.000000  : :  Sine  of  A,  33°  15'  9.739013 


12.511883 
9.922355 


12.250896 
9.922355 


Hyp.  388.6  2.589528  :  leg.  B,  C.  2131       2.328541 

NOTE.     If  the  leg  B  C  had   been  given,  instead  of  the  leg 

A  B,  the  proportions  would  have   been  the  same,  the 

obvious  changes  being  made. 


BY  NATURAL  SINES. 

To  solve  this  CASE  by  natural  sines,  institute  the  follow- 
ing proportions  : 

To  find  the  hypothenuse.     As  THE  NATURAL  SINE  OF  THE 

ANGLE  OPPOSITE  THE  GIVEN  LEG,  IS  TO  THE  LENGTH  OF  THE 
LEG,  SO  IS  UNITY,  OR  1,  TO  THE  LENGTH  OF  THE  HYPOTHE- 
NUSE. 

Or,  which  is  the  same  thing,  DIVIDE  THE  GIVEN  LEG  BY 

THE  NATURAL  SINE  OF  ITS  OPPOSITE  ANGLE,  AND  THE  QUO- 
TIENT WILL  BE  THE  HYPOTHENUSE. 

To  find  the  other  leg.  As  THE  NATURAL  SINE  OF  THE  AN- 
GLE OPPOSITE  THE  GIVEN  LEG,  IS  TO  THE  LENGTH  OF  THE 
GJVEN  LEG,  SO  IS  THE  NATURAL  SINE  OF  THE  ANGLE  OPPO- 
SITE THE  OTHER  LEG,  TO  THE  LENGTH  OF  THE  OTHER  LEG. 

EXAMPLE. 

Given  leg  325.  Nat.  sine  of  56°  45',  the  angle  opposite 
the  given  leg,  0.83629.  Nat.  sine  of  33°  15',  the  angle  op- 
posite the  other  leg,  0.54829. 

As  0.83629  :  325  :  :  1  :  388.6. 

As  0.83629  :  325  ::  0.54829  :  213.07. 


TRIGONOMETRY.  29 


CASE   III. 


The  hypothenuse  and  one  leg  given,  to 
find  the  angles  and  the  other  leg.    Fig.  44. 


In  the  triangle  A  C  B,  given  the  hypothenuse  A  C  50,  and 
the  leg  A  B  40,  to  find  the  angles  and  leg  B  C. 

Making  the  hypothenuse  radius,  the  proportion  to  find  the 
angle  A  C  B  will  be  : 


As  hyp.  50 
:  radius 
:  :  leg  A  B  40  - 

1.698970 
10.000000 
1.602060 

11.602060 
1.698970 

:  sine  A  C  B,  53°  8'        9.903090 


The  angle  A  C  B  being  53°  8',  the  other  is  consequently 
36°  52'. 

The  angles  being  found,  the  leg  B  C  may  be  found  by 
either  of  the  preceding  CASES.  It  is  30. 


BY  NATURAL  SINES. 

The  angle  opposite  the  given  leg,  may  be  found  by  the  fol- 
lowing proportion : 

As  THE  HYPOTHENUSE  IS  TO  UNITY,  OR  1,  SO  IS  THE  GIVEN 
LEO  TO  THE  NAT.  SINE  OF  ITS  OPPOSITE  ANGLE. 

Or,  which  is  the  same  thing,  DIVIDE  THE  GIVEN  LEG  BY  THE 

HYPOTHENUSE,  AND  THE  QUOTIENT  WILL  BE  THE  NAT.  SINE. 
EXAMPLE. 

The  leg  A  B  40,  divided  by  the  hypothenuse  50,  gives  a 


30  TRIGONOMETRY. 

quotient  0.80000 ;  which,  looking  in  the  table  of  nat.  sines, 
the  nearest  corresponding  number  of  degrees  and  minutes  will 
be  found  to  be  53°  8',  the  angle  A  C  B. 


BY  THE  SQUARE  ROOT. 

In  this  CASE  the  required  leg  may  be  found  by  the  square 
root,  without  finding  the  angles ;  according  to  the  following 
PROPOSITION  : 

IN  EVERY  RIGHT  ANGLED  TRIANGLE,  THE  SQUARE  OF  THE 
HYPOTHENUSE  IS  EQUAL  TO  THE  SUM  OF  THE  SQUARES  OF 
THE  TWO  LEGS.  Hence, 

THE  SQUARE  OF  THE  GIVEN  LEG  BEING  SUBSTRACTED 
FROM  THE  SQUARE  OF  THE  HYPOTHENUSE,  THE  REMAINDER 
WILL  BE  THE  SQUARE  OF  THE  REQUIRED  LEG. 

As  in  the  preceding  EXAMPLE;  the  square  of  the  leg  A  B 
40  is  1600 ;  this  substracted  from  the  square  of  the  hypothe- 
nuse  50,  which  is  2500,  leaves  900,  the  square  of  the  legBC, 
the  square  root  of  which  is  30,  the  length  of  leg  B  C,  as  found 
by  logarithms. 


CASE    IV. 


The  legs  given,  to  find  the  angles  and 
hypothenuse.     Fig.  45. 


73.7 


In  the  triangle  A  B  C,  given  the  leg  A  B  78.7,  and  the  leg 
B  C  89  ;  to  find  the  angles  and  hypothenuse. 

Making  the  leg  A  B  radius,  the  proportion  to  find  the  angle 
BAG  will  be, 


TRIGONOMETRY.  31 

As  leg  A  B,  78.7     -       1.895975 
:  radius     -  10.000000 

:  :  leg  B  C,  89       -       1.949390 

11.949390 

1.895975 


:  tariff.  BAG,  48°  31'  10.053415 


The  angle  A  C  B  is  consequently  41°  29'. 

Making  the  leg  B  C  radius,  the  proportion  to  find  the  angle 
B  C  A  will  be  similar,  with  the  obvious  differences. 

The  angles  being  found,  the  hypothenuse  may  be  found  by 
CASE  II.  It  is  nearest  1 19. 


BY  THE  SQUARE  ROOT 

In  this  case,  the  hypothenuse  may  be  found  by  the  square 
root,  without  finding  the  angles ;  according  to  the  following 

PROPOSITION. 

IN  EVERY  RIGHT  ANGLED  TRIANGLE,  THE  SUM  OF  THE 
SQUARES  OF  THE  TWO  LEGS  IS  EQUAL  TO  THE  SQUARE  OF 
THE  HYPOTHENUSE. 

In  the  above  EXAMPLE,  the  square  of  A  B  78.7  is  6193.69, 
the  square  of  B  C  89  is  7921 ;  these  added  make  14114.69, 
the  square  root  of  which  is  nearest  1 19. 


BY  NATURAL  SINES. 


The  hypothenuse  being  found  by  the  square  root,  the  angles 
may  be  found  by  nat.  sines,  according  to  the  preceding  CASE. 


32  TRIGONOMETRY. 

Hyp.      Leg  B  C.  Nat.  Sine. 

119)    89.00000  (74789 
83.3 


570  The   nearest   degrees    and    minutes 

476  corresponding  to  the  above  nat.    sine, 

are  48°  24',  for  the  angle  BAG.    The 

940  difference  between  this  and  the  angle, 

833  as  found  by  logarithms,   is   occasioned 

by  dividing  by  119,  which  is  not  the 

1070  exact    length   of    the   hypothenuso    it 

952  being  a  fraction  too  much. 


1180 
1071 

109 


BY  NATURAL  TANGENTS. 

Leg  A  B.        Rad.  B.  C. 

78,7     :        1       :  :         89.0 
89.0 

Nat.  Tang. 

78.7)  89.0  (:    1.13087=48°  31' 

787 

1030 

787 

2430 
2361 

6900 
6296 

6040 
5509 


TRIGONOMETRY. 


33 


PART      II. 

OBLIQUE  TRIGONOMETRY. 

The  solution  of  the  first  two  CASES  of  Oblique  Trigonom- 
etry depends  on  the  following-  PROPOSITION. 

IN  ALL  PLANE  TRIANGLES,  THE  SIDES  ARE  IN  PROPORTION 
TO  EACH  OTHER,  AS  THE  SINES  OF  THEIR  OPPOSITE  ANGLES. 

THAT  is,  AS  THE  SINE  OF  ONE  ANGLE   is  TO  ITS  OPPOSITE 

SIDE,  SO  IS  THE  SINE  OF  ANOTHER  ANGLE  TO  ITS  OPPOSITE 
SIDE.  OR,  AS  ONE  SIDE  IS  TO  THE  SINE  OF  ITS  OPPOSITE 
ANGLE,  SO  IS  ANOTHER  SIDE  TO  THE  SINE  OF  ITS  OPPOSITE 
ANGLE. 

NOTE.  When  an  angle  exceeds  90°,  make  use  of  its  sup- 
plement, which  is  what  it  wants  of  180°.  Note,  Def. 
25.  GEOM. 


CASE    I. 


The  angles  and  one  side  given,  to  find  the 
other  sides.     Fig-  46. 


Fig.  46. 
C 


B 


In  the  triangle  ABC,  given  the  angle  at  B  48°,  the  angle 
at  C  72°,  consequently  the  angle  at  A  60°,  and  the  side  A  B 
200,  to  find  the  sides  A  C  and  B  C. 


To  find  the  side  AC. 
As  sine  A  C  B,  72°    9.978206 
:  side  AB,  200     -      2.301030 
:  :  sine  ABC,  48°  -9.871073 


12.172103 
9.978206 


side  AC,  156     -     2.193897 


To  find  the  side  B  C. 
As  sine  A  C  B,  72°  -  9.978206 
:side  AB,  200        -  2.301030 
:  :  sineB  AC,  60° -9.937531 


12.328561 
9.978206 

:  sideB  C,  182    -     2.260355 


34 


TRIGONOMETRY. 


BY  NATURAL  SINES. 

AS  THE  NAT.  SINE  OF  THE  ANGLE  OPPOSITE  THE  GIVEN 
SIDE  IS  TO  THE  GIVEN  SIDE,  SO  IS  THE  NAT.  SINE  OF  THE  AN- 
GLE OPPOSITE  EITHER  OF  THE  REQUIRED  SIDES  TO  THAT 
REQUIRED  SIDE. 

Given  side  200 ;  nat.  sine  of  72°,  its  opposite  angle,  0.951 15  ; 
nat.  sine  of  ABC  48°,  0.74314;  nat.  sine  of  B  A  C  60°1 
0.86617.  Thus, 

0.95115  :  200  :   :  0.74314  :   156. 

0.95115   :  200  :  :  0.86617  :   182, 


CASE    II. 


Two  sides,  and  an  angle  opposite  to  one 
of  them  given,  to  find  the  other  angles  and 
side.  Fig.  47. 


In  the  triangle  ABC,  given  the  side  A  B  240,  the  side  B  *G 
200,  and  the  angle  at  A  46°  30' ;  to  find  the  other  angles  and 
the  side  A  C. 

To  find  the  angle  A  C  B. 
As  sideB  C,  200    -     2.301030 
:  sine  B  AC,  46°  30'  9.860562 
:  :  side  AB,  240  -       2.380211 


12.240773 
2.301030 


:sineACB,60°30'  nearly9.939743 


Angle  at  A 
C 


46°  30' 
60    30 


107.00 


Sum  of  the  three  angles  180° 


Sum  of  two 
Angle  at  B 


107° 
73 


The  side  A  C  will  be  found  by  CASE  I.  to  be  nearest  253. 

NOTE.  If  the  given  angle  be  obtuse,  the  angle  sought 
will  be  acute ;  but  if  the  given  angle  be  acute,  and  op- 
posite a  given  lesser  side,  then  the  angle  found  by  the 
operation  may  be  either  obtuse  or  acute.  It  ought 
therefore  to  be  mentioned  which  it  is,  by  the  conditions 
of  the  question. 


TRIGONOMETRY.  35 


BY  NATURAL  SINES. 

As  THE  SIDE  OPPOSITE  THE  GIVEN  ANGLE  IS  TO  THE  NAT. 
SINE  OF  THAT  ANGLE,  SO  IS  THE  OTHER  GIVEN  SIDE  TO  THE 
NAT.  SINE  OF  ITS  OPPOSITE  ANGLE. 

One  given  side  200,  nat.  sine  of  46°  30',  its  opposite  an- 
gle, 0.72537,  the  other  given  side  240. 

As  200  :  0.72537  :  :  240  :  0.87044=60°  30'. 


CASE    III. 


Two  sides  and  their  contained  angle 
given,  to  find  the  other  angles  and  side. 
Fig.  48. 

The  solution  of  this  CASE  depends  on  the  following  PROP- 
OSITION. 

IN  EVERY  PLANE  TRIANGLE,  AS  THE  SUM  OF  ANY  TWO 
SIDES  ISTO  THEIR  DIFFERENCE,  SOIS  THE  TANGENT  OF  HALF 
THE  SUM  OF  THE  TWO  OPPOSITE  ANGLES  TO  THE  TANGENT 
OF  HALF  THE  DIFFERENCE  BETWEEN  THEM. 

ADD  THIS  HALF  DIFFERENCE  TO  HALF  THE  SUM  OF  THE 
ANGLES,  AND  YOU  WILL  HAVE  THE  GREATER  ANGLE,  AND 
SUBSTRACT  THE  HALF  DIFFERENCE  FROM  THE  HALF  SUM, 
AND  YOU  WILL  HAVE  THE  LESSER  ANGLE. 

In  the  triangle  ABC,  given  the  side  A  B  240,  the  side  A  C 
180,  and  the  angle  at  A  36°  40',  to  find  the  other  angles  and 
side. 

Side  A  B  -          240  A  B  -  240 

A  C  -  180  AC  -  180 


Sum  of  the  two  sides  420  Difference  60 

The  given  angle  BAG  36°  40',  substracted  from  180°,  leaves 
143°  20',  the  sum  of  the  other  two  angles,  the  half  of  which 
is  71°  40'. 


TRIGONOMETRY. 


As  the  sum  of  two  sides,  420 
:  their  difference  60  - 
:  :  tangent  half  unknown  ang.  71°  40' 


:  tangent  half  difference,  23°  20'  nearly 

The  half  sum  of  the  two  unknown  angles, 
The  half  difference  between  them, 

Add,  gives  the  greater  angle  A  C  B 
Substract,  gives  the  lesser  angle  ABC 

The  side  B  C  may  be  found  by  CASE  I.  or  II. 


2.623249 

1.778151 

10.479695 

12.257846 
2.623249 


9.634597 

71°  40' 
23    20 

95    00 

48    23 


CASE    IV. 


The  three  sides  given,  to  find  the 
Fig.  49. 


A        105         B          B 

The  solution  of  this  CASE  depends  on  the  following  PROP- 
OSITION. 

IN  EVERY  PLANE  TRIANGLE,  AS  THE  LONGEST  SIDE  IS  TO 

THE  SUM  OF  THE  OTHER  TWO  SIDES,  SO  IS  THE  DIFFERENCE 
BETWEEN  THOSE  TWO  SIDES  TO  THE  DIFFERENCE  BETWEEN 
THE  SEGMENTS  OF  THE  LONGEST  SIDE,  MADE  BY  A  PERPEN- 
DICULAR LET  FALL  FROM  THE  ANGLE  OPPOSITE  THAT  SIDE 

Half  the  difference  between  these  segments,  added  to  half 
the  sum  of  the  segments,  that  is,  to  half  the  length  of  the 
longest  side,  will  give  the  greatest  segment ;  and  this  half 
difference  substracted  from  the  half  sum  will  be  the  lesser 
segment.  The  triangle  being  thus  divided,  becomes  two 
right  angled  triangles,  in  which  the  hypothenuse  and  one  leg 
are  given  to  find  the  angles. 


TRIGONOMETRY. 


37 


In  the  triangle  ABC,  given  the  side  A  B  105,  the  side  A  G 
85,  and  the  side  B  C  50,  to  find  the  angles. 

Side  A  C          -         85  AC  85 

B  C          -          50  B  C  50 


Sum  of  the  two  sides  135 

As  the  longest  side  A  B,  105 
:  sum  of  the  other  two  sides,  135 
:  :  difference  between  those  sides,  35 


:  difference  between  the  segments,  45 

Half  the  side  A  B 

Half  the  difference  of  the  segments 

Add,  gives  the  greater  segment  A  D 


Difference        35 


2.021189 
2.130334 
1.544068 

3.674402 
2.021189 

1.653213 

-  52.5 

-  22.5 

-  75.0 


Substract,  gives  the  lesser  segment  B  D  30.0 

Thus  the  triangle  is  divided  into  two  right  angled  trian- 
gles, ADC  and  B  D  C ;  in  each  of  which  the  hypothenuse 
and  one  leg  are  given  to  find  the  angles. 


To  find  the  angle  D  C  A. 


As  hyp.  A  C,  85 

:  radius 

:  :  seg.  A  D,  75 


1.929419 

10.000000 

1.875061 


11.875061 
1.929419 


:  sine  DC  A,  61°  56'  9.945642 


To  find  the  angle  D  C  B. 
As  hyp.  BC,  50  -     1.698970 
:  radius       -       -      10.000000 
::seg.  B  D,  30     -     1.477121 

11.477121 
1.698970 

:  sine  DCB,  36°  52'  9.778151 


The  angle  D  C  A  61°  56',  substracted  from  90°,  leaves  the 
angle  C  A  D  28°  4'. 

The  angle  D  C  B  36°  52',  substracted  from  90°,  leaves  the 
angle  CBD530  16'. 

The  angle  D  C  A  6 1  °  56',  added  to  the  angle  D  C  B  36°  52', 
gives  the  angle  A  C  B  98°  48'. 

This  CASE  may  also  be  solved  according  to  the  following 
PROPOSITION. 

IN  EVERY  PLANE  TRIANGLE,  AS  THE  PRODUCT  OF  ANY  TWO 
SIDES  CONTAINING  A  REQUIRED  ANGLE  IS  TO  THE  PRODUCT 
4* 


38  TRIGONOMETRY. 

OF  HALF  THE  SUM  OF  THE  THREE  SIDES,  AND  THE  DIFFER- 
ENCE BETWEEN  THAT  HALF  SUM  AND  THE  SIDE  OPPOSITE 
THE  ANGLE  REQUIRED,  SO  IS  THE  SQUARE  OF  RADIUS  TO  THE 
SQUARE  OF  THE  CO-SINE  OF  HALF  THE  ANGLE  REQUIRED. 


Those  who  make  themselves  well  acquainted  with  TRIGO- 
NOMETRY, will  find  its  application  easy  to  many  useful  purpo- 
ses, particularly  to  the  mensuration  of  heights  and  distances. 
These  are  here  omitted,  because  as  this  work. is  designed  prin- 
cipally to  teach  the  art  of  common  FIELD-SURVEYING,  it  was 
thought  improper  to  swell  its  size,  and  consequently  in- 
crease its  price,  by  inserting  any  thing  not  particularly  con- 
nected with  that  art. 

It  is  recommended  to  those  who  design  to  be  surveyors,  to 
study  TRIGONOMETRY  thoroughly ;  for  though  a  common  field 
may  be  measured  without  an  acquaintance  with  that  science, 
yet  many  cases  will  occur  in  practice,  where  a  knowledge  of 
it  will  be  found  very  beneficial ;  particularly  in  dividing 
land,  and  ascertaining  the  boundaries  of  old  surveys.  In- 
deed no  one  who  is  ignorant  of  TRIGONOMETRY,  can  be  an 
accomplished  surveyor. 


SURVEYING. 


SURVEYING  is  the  art  of  measuring,  laying  out,  and  di- 
viding land. 

PART  I. 

MEASURING  LAND. 

The  most  common  measure  for  land  is  the  acre ;  which 
contains  160  square  rods,  poles,  or  perches;  or  4  square 
roods,  each  containing  40  square  rods. 

The  instrument  most  in  use,  for  measuring  the  sides  of 
fields,  is  GUNTER'S  chain,  which  is  in  length  4  rods,  or  66 
feet;  and  is  divided  into  100  equal  parts,  called  links,  each 
containing  7  inches  and  92  hundredths.  Consequently,  1 
square  chain  contains  16  square  rods,  and  ten  square  chains 
make  1  acre. 

In  small  fields,  or  where  the  land  is  uneven,  as  is  the  case 
with  a  great  part  of  the  land  in  New  England,  it  is  better  to 
use  a  chain  of  only  two  rods  in  length,  as  the  survey  can 
be  more  accurately  taken.* 


SECTION    I. 
PRELIMINARY  PROBLEMS. 

PROBLEM  I.  To  reduce  two  rod  chains  to  four  rod 
chains. 

RULE.  If  the  number  of  two  rod  chains  be  even,  take 
half  the  number  for  four  rod  chains,  and  annex  the  links,  if 
any;  thus,  16  two  rod  chains  and  37  links,  make  8  four  rod 
chains  and  37  links. 

But  if  the  number  of  chains  be  odd,  take  half  the  greatest 
even  number  for  chains,  and  for  the  remaining  number  add 
50  to  the  link  :  Thus,  17  two  rod  chains  and  42  links  makes 
8  four  rod  chains  and  92  links. 

PROBLEM  II.  To  reduce  two  rod  chains  to  rods  and  de- 
cimal parts. 

*  As  there  is  no  standard  of  long  measure  established  by  the  General 
Government,  the  standard  yard,  which  is  kept  in  the  State  Treasurer's 
office,  is  adopted  as  a  standard  of  long  measure  for  Connecticut. 
Each  chain  6f  2  rods,  should  be  11,  and  each  of  4  rods,  22  yards,  in 
length. 


40  SURVEYING. 

RULE.  Multiply  the  chains  by  2,  and  the  links  by  4, 
which  will  give  hundredths  of  a  rod;  thus,  17  two  rod  chains 
and  21  links,  make  34  rods  and  84  hundredths ;  expressed 
thus,  34.84  rods. 

If  the  links  exceed  25,  add  one  to  the  number  of  rods,  and 
multiply  the  excess  by  4:  thus,  15  two  rod  chains  and  38 
links  make  31.52  rods. 

PROBLEM  III.  To  reduce  four  rod  chains  to  rods  and 
decimal  parts. 

RULE.  Multiply  the  chains,  or  chains  and  links,  by  4 ; 
the  product  will  be  rods  and  hundredths :  thus,  8  chains  and 
64  links,  make  34.56  rods. 

NOTE.  The  reverse  of  this  rule,  that  is,  dividing  by  4,  will  reduce 
rods  and  decimals  to  chains  and  links:  thus,  105.12  rods,  make  26 
chains  and  28  links. 

PROBLEM  IV.      To  reduce  square  rods  to  acres. 

RULE.  Divide  the  rods  by  160,  and  the  remainder  by  40, 
if  it  exceeds  that  number,  for  roods  or  quarters  of  an  acre : 
thus  746  square  rods  make  4  acres,  2  roods,  and  26  rods. 

PROBLEM  V.      To  reduce  square  chains  to  acres. 

RULE.  Divide  by  10;  or,  which  is  the  same  thing-,  cut 
off  the  right  hand  figure :  thus,  1460  square  chains  make 
146  acres;  and  846  square  chains  make  84  acres  and  6 
tenths. 

PROBLEM  VI.      To  reduce  square  links  to  acres. 

RULE.  Divide  by  100000;  or,  which  is  the  same  thing, 
cutoff  the 5  right  hand  figures  :  thus,  3845120  square  links 
make  38  acres  and  45120  decimals. 

NOTE.  When  the  area  of  a  field,  by  which  is  meant  its  superficial 
contents,  is  expressed  in  square  chains  and  links,  the  whole  may 
be  considered  as  square  links,  and  the  number  of  acres  contained 
in  the  field,  found  as  above.  Then  multiply  the  figures  cut  off  by 
4,  and  again  cut  off  5  figures,  and  you  have  the  roods  ;  multiply  the 
figures  last  cut  off  by  40,  and  again  cut  off  5  figures,  and  you  have 
the  rods. 

EXAMPLE.  How  many  acres,  roods,  and  rods,  are  there  in  156 
square  chains  and  3274  square  links  1 

15)63274  square  links. 
4 

2)53096 
40 


21)23840 
Answer.    15  acres  2  roods  and  21  rods. 

PROBLEMS  for  finding  the  area  of  right  lined  figures,  and 
also  of  circles. 


SURVEYING.  41 

PROBLEM  VII.  To  find  the  area  of  a  square  or  rectan- 
gle. 

RULE.  Multiply  the  length  into  the  breadth ;  the  product 
will  be  the  area. 

PROBLEM  VIII.  To  find  the  area  of  a  rhombus  or 
rhomboid. 

RULE.  Drop  a  perpendicular  from  one  of  the  angles  to 
its  opposite  side,  and  multiply  that  side  into  the  perpendicu- 
lar; the  product  will  be  the  area. 

PROBLEM  IX.      To  find  the  area  of  a  triangle. 

RULE  1.  Drop  a  perpendicular  from  one  of  the  angles  to 
its  opposite  side,  which  maybe  called  the  base;  then  mul- 
tiply the  base  by  half  the  perpendicular,  or  the  perpendicu- 
lar by  half  the  base  ;  the  product  will  be  the  area.  Or,  mul- 
tiply the  whole  base  by  the  whole  perpendicular,  and  half 
the  product  will  be  the  area. 

RULE  2.  If  it  be  a  right  angled  triangle,  multiply  one  of 
the  legs  into  half  the  other ;  the  product  will  be  the  area. 
Or,  multiply  the  two  legs  into  each  other,  and  half  the 
product  will  be  the  area. 

RULE  3,  When  the  three  sides  of  a  triangle  are  knownr 
the  area  may  be  found  arithmetically,  as  follows  : 

Add  together  the  three  sides  ;  from  half  their  sum  substract 
each  side,  noting  down  the  remainders;  multiply  the  half 
sum  by  one  of  those  remainders,  and  that  product  by  another 
remainder,  and  that  product  by  the  other  remainder;  the 
square  root  of  the  last  product  will  be  the  area.* 

EXAMPLE.  Suppose  a  triangle  whose  three  sides  are  24, 
20,  and  18  chains.  Demanded  the  area. 

24+204-18=62,  the  sum  of  the  three  sides,  the  half  of 
which  is  31.  From  31  substract  24,  20,  and  18;  the  three 
remainders  will  be  7,  11,  and  13. 

31X7=217;  217x11=2387;  2387X1 3=  3 1031,  the  square 
root  of  which  is  176.1,  or  17  acres,  2  roods,  and  17  rods. 

BY  LOGARITHMS. 

As  the  addition  of  logarithms  is  the  same  as  the  multipli- 
cation of  their  corresponding  numbers ;  and  as  the  number 
answering  to  one  half  of  a  logarithm  will  be  the  square  root 
of  the  number  corresponding  to  that  logarithm  :  it  follows, 
that  if  the  logarithm  of  the  half  sum  of  the  three  sides,  and 

*  Better  expressed  thus.  From  half  the  sum  of  the  sides  substract 
each  side  separately.  Multiply  the  half  sum  and  the  several  re- 
mainders together,  and  the  square  root  of  the  product  will  be  the 
area. — ED. 


42  SURVEYING. 

the  logarithms  of  the  three  remainders,  be  added  together, 
the  number  corresponding  to  one  half  the  sum  of  those  loga- 
rithms will  be  the  area  of  the  triangle. 

The  half  sum,  31  1.491362 

The  first  remainder,  7  -  0.845098 

The  second  remainder,  1 1  1.041393 

The  third  remainder,  13  1.11 3943 

The  square  of  the  area,  31030.083  nearly          4.491796 
Area,  176  square  chains  150  square  links  2.245898 

RULE  4.  When  two  sides  of  a  triangle,  and  their  contained 
angle,  that  is,  the  angle  made  by  those  sides,  are  given,  the 
area  may  be  found  as  follows  : 

Add  together  the  logarithms  of  the  two  sides,  and  the  loga- 
rithmic sine  of  the  angle ;  from  their  sum  substract  the  lo- 
garithm of  radius,  the  remainder  will  be  the  logarithm  of 
double  the  area. 

EXAMPLE.  Suppose  a  triangle,  one  of  whose  sides  is  105 
rods,  and  another  85,  and  the  angle  contained  between  them 
28°  5'.  Demanded  the  area. 

One  side,  105  -         2.021189 

The  other  side,  85    -  -  1.929419 

Sine  angle,  28°  5'     -  9.672795 

13.623403 
Substract  radius      -  -         10.000000 


Double  area,  4200  rods  nearly  3.623403 

Answer,  2 100  rods. 

NOTE.  Radius  may  be  subtracted  by  cancelling  the  left  hand  figure 
of  the  index,  or  substracting  10,  without  the  trouble  of  setting  down 
the  ciphers. 


BY  NATURAL  SINES. 


Multiply  the  two  given  sides  into  each  other,  and  that  pro- 
duct by  the  natural  sine  of  the  given  angle ;  the  last  product 
will  be  double  the  area  of  the  triangle. 

Nat.  sine  of  the  angle  28°  5',  0.47076. 

105X85=8925,  and  8925X0.47076=4201,  the  double  area 
of  the  triangle. 

PROBLEM  X.     To  find  the  area  of  a  trapezoid. 


SURVEYING.  43 

RULE.  Multiply  half  the  sum  of  the  two  parallel  sides 
by  the  perpendicular  distance  between  them,  or  the  sum  of 
the  two  parallel  sides  by  half  the  perpendicular  distance,  the 
product  will  be  the  area. 

PROBLEM  XI.  To  find  the  area  of  a  trapezium,  or  ir- 
regular four  sided  figure. 

RULE.  Draw  a  diagonal  between  two  opposite  angles, 
which  will  divide  the  trapezium  into  two  triangles.  Find 
the  area  of  each  triangle,  and  add  them  together.  Or,  multi- 
ply the  diagonal  by  half  the  sum  of  the  two  perpendiculars 
let  fall  upon  it,  or  the  sum  of  the  two  perpendiculars  by  half 
the  diagonal,  the  product  will  be  the  area. 

NOTE.  Where  the  length  of  the  four  sides  and  of  the  diagonal  is 
known,  the  area  of  the  two  triangles,  into  which  the  trapezium  is 
divided,  may  be  calculated  arithmetically,  according  to  PROS.  IX. 
Rule  3. 

PROBLEM  XII.  To  find  the  area  of  a  figure  containing 
more  than  four  sides. 

RULE.  Divide  the  figure  into  triangles,  and  trapezia,  by 
drawing  as  many  diagonals  as  are  necessary,  which  diago- 
nals must  be  so  drawn  as  not  to  intersect  each  other  ;  then 
find  the  area  of  each  of  the  several  triangles  or  trapezia,  and 
add  them  together ;  the  sum  will  be  the  area  of  the  whole 
figure. 

NOTE.  A  little  practice  will  suggest  the  most  convenient  way  of 
drawing  the  diagonals,  but  whichever  way  they  are  drawn,  pro- 
vided they  do  not  intersect  each  other,  the  whole  area  will  be 
found  the  same. 

PROBLEM  XIII.     Respecting  circles. 

RULE  1.  If  the  diameter  be  given,  the  circumference  may 
be  found  <foy  one  of  the  following  proportions  :  as  7  is  to  22, 
or  more  exactly,  as  113  is  to  355,  or  in  decimals,  as  I  is  to 
3.14159,  so  is  the  diameter  to  the  circumference. 

RULE  2.  If  the  circumference  be  given,  the  diameter  may 
be  found  by  one  of  the  following  proportions :  as  22  is  to  7, 
or  as  355  is  to  113,  or  as  1  is  to  0,31831,  so  is  the  circum- 
ference to  the  diameter. 

RULE  3.  The  diameter  and  circumference  being  known, 
multiply  half  the  one  into  half  the  other,  and  the  product 
will  be  the  area. 

RULE  4.  From  the  diameter  only,  to  find  the  area  :  mul- 
tiply the  square  of  the  diameter  by  0.7854,  and  the  product 
will  be  the  area. 

RULE  5,     From  the  circumference  only  to  find  the  area : 


44  SURVEYING. 

multiply  the  square  of  the  circumference  by  0.07958,  and  the 
product  will  be  the  area. 

RULE  6.  The  area  being  given,  to  find  the  diameter :  di- 
vide the  area  by  0.7854,  and  the  quotient  will  be  the  square 
of  the  diameter ;  from  this  extract  the  square  root,  and  you 
will  have  the  diameter. 

RULE  7.  The  area  being  given,  to  find  the  circumference  : 
divide  the  area  by  0.07958,  and  the  quotient  will  be  the 
square  of  the  circumference ;  from  this  extract  the  square  root, 
and  you  will  have  the  circumference. 

To  find  the  area  of  an  Ellipse  or  an  Ellipsis 

RULE.  Multiply  the  product  of  the  two  diameters  by 
0.7854,  and  point  off  from  the  product  as  many  figures  at  the 
right  hand  as  there  are  decimals  in  both  factors,  and  those 
at  the  left  will  be  the  area  of  the  figure. 

EXAMPLE.  What  is  the  area  of  an  ellipse,  of  which  the 
longest  diameter  is  65  rods  and  10  links,  and  the  shortest  is 

45  rods  and  10  links. 

Longest  diameter,  65.4 
Shortest  diameter,  45.4 

2616 
3270 
2616 

2969.16 

.7854 


1187664 
1484580 
2375328 
2078412 

2331.978264 
1 


160)2332(14 
160 


732 
740 

92 
A.  Q.R. 

Answer,  14  2  12 


SURVEYING.  45 

SECTION  II. 

The  following  CASES  teach  the  most  usual  methods  of 
taking  the  survey  of  fields ;  also,  how  to  protract  or  draw  a 
plot  of  them,  and  to  calculate  their  area. 

NOTE.  The  field  book  is  a  register  containing  the  length  of  the  sides  of 
a  field,  as  found  by  measuring  them  with  a  chain ;  also,  the  bear- 
ings, or  courses  of  the  sides,  or  the  quantity  of  the  several  angles, 
as  found  by  a  compass  or  other  instrument  for  that  purpose ; 
together  with  such  remarks  as  the  surveyor  thinks  proper  to  make 
in  the  field. 


CASE  I. 


TO  SURVEY  A  TRIANGULAR  FIELD. 

Measure  the  sides  of  a  field  with  a  chain,  and  enter  their 
several  lengths  in  a  FIELD-BOOK  ;  protract  the  field  on  paper, 
and  then  find  the  area  by  PROB.  IX.  Rule  1.  Or,  without 
plotting  the  field,  calculate  the  area  by  PROS.  IX.  Rule  3. 

Fig.  50. 
FIELD  BOOK.     See  Fig.  50.        c 

Chains. 

AB       -  20 

BC       -        -        24  .. 

CA      -        .         18  **         D 

To  find  the  area,. 
Ch.  L. 

BaseBC    -    -     24.00 
Half  perp.  A  D  .       7.34 


VOCh. 


9600 
7200 
16800 

Acres  17)61600 
4 


Roods  2)46400 
40 

Rods  18)56000 

Acres  Roods  Rods 
Area  17—2—18.56 
5 


46  SURVEYING. 

NOTE.  When  there  are  ciphers  at  the  right  hand  of  the  links,  they 
may  be  rejected ;  remembering  to  cut  off  a  proper  number  of 
figures  according  to  decimal  rules. 

Observe,  That  in  measuring  with  a  chain,  slant  or  inclined 
surfaces,  as  the  sides  of  hills,  should  be  measured  horizon- 
tally, and  not  on  the  plane  or  surface  of  the  hill;  otherwise, 
a  survey  cannot  be  accurately  taken.  To  effect  this,  the 
lower  end  of  the  chain  must  be  raised  from  the  ground,  so 
as  to  have  the  whole  in  a  horizontal  line;  and  the  end  thus 
raised  must  be  directly  over  the  point  where  the  chain  be- 
gins or  ends,  according  as  you  are  ascending  or  descending 
a  hill ;  which  point  may  be  ascertained  by  a  plummet  and  line. 


CASE  II. 
TO  SURVEY  A  FIELD  IN  THE  FORM  OF  A  TRAPEZIUM. 

Measure  the  several  sides,  and  a  diagonal  between  two  op- 
posite angles ;  protract  the  field,  and  find  the  area  by  PROB- 
LEM XL  Or,  without  protracting  the  field,  calculate  the 
area  according  to  the  note  at  the  end  of  that  PROBLEM. 

Fig.  51. 
FIELD-BOOK.     See  Fig.  51. 

Ch.  L. 

AB  -  27.50 
BC  -  11.70 
CD  -  21.50 
DA  -  14.70 
Diag.  AC  -  28. 


TO  PROTRACT  THIS  TRAPEZIUM. 

Draw  the  side  A  B,  the  given  length ;  with  the  diagonal 
A  C  28,  and  the  side  B  C  11.70,  describe  cross  arcs  as  at  C, 
from  A  and  B  as  centres;  and  the  point  of  intersection  will 
represent  that  corner  of  the  field :  then,  with  the  side  C  D 
21.50,  and  the  side  A  D  14.70,  describe  cross  arcs  as  at  D,  from 
A  and  C  as  centres ;  and  the  point  of  intersection  will  repre- 
sent that  corner  of  the  field. 


SURVEYING. 


TO  FIND  THE  AREA. 


Perpendicular  B  a  -  -  11.34 

Dm  11.10 

22.44 
Half  diagonal  A  C  14.00 

897600 
2244 

Acres  31)416 
4 

Rood  1)664 
40 

Rods  26)560 
Acres  Rood  Rods 
'Area  31— 1—26.56 


NOTE.  The  perpendiculars  need  not  be  actually  drawn ;  their  length 
may  be  obtained  as  follows :  from  the  angle  opposite  the  diagoaal 
open  the  dividers  so  as  when  one  foot  is  in  the  angular  point,  as 
at  B,  the  other,  being  moved  backwards  and  forwards,  may  just 
touch  the  diagonal  at  A,  and  neither  go  the  least  above  or  below 
it;  that  distance  in  the  dividers  being  measured  on  the  scale,  will 
give  the  length  of  the  perpendicular. 


CASE    III. 

TO    SURVEY   A  FIELD  WHICH  HAS    MORE    THAN  FOUR  SIDES, 
BY  THE  CHAIN  ONLY. 

Measure  the  several  sides,  and  from  some  one  of  the  angles 
from  which  the  others  may  be  seen,  measure  diagonals  to 
them ;  draw  a  plot  of  the  field,  and  find  the  area  bv  PROB- 
LEM XII. 


FIELD-BOOK.     See  Fig.  52 


56?     £tf 

Ch.L, 

AB  -  •        30.60  Diagonals. 

B  C  -  -        20.40          -          -          -          Ch.  L 

CD  -  -        22.40  AC  -          -  45. 

DE  -  -         16.20  AD-          -          -          35. 

EF  -  -         13.50  AE  -          -          -          24.20 

FA  -  -        28. 


TO  PROTRACT  THIS  FIELD. 


Draw  the  side  AB,  making  it  the  given  length  30.60; 
with  the  diagonal  A  C  45,  and  the  side  B  C  20.40,  describe 
cross  arcs  as  at  C,  from  the  points  A  and  B  as  centres,  and 
the  point  of  intersection  will  represent  that  corner  of  the 
field  ;  draw  the  side  B  C,  and  the  dotted  diagonal  A  C ;  with 
the  diagonal  A  D  35,  and  the  side  C  D  22.40,  describe  cross 
arcs  as  at  D,  from  the  points  A  and  C,  and  draw  the  side  C  D, 
and  the  dotted  diagonal  A  D.  Proceed  in  this  manner  till- 
all  the  sides  and  diagonals  are  drawn. 


TO  FIND  THE  AREA. 


The  field  heing  plotted,  may  he  divided  into  one  trapezium 
and  two  triangles ;  the  area  of  which  is  calculated  as  fol- 
lows : 


SURVEYING. 


49 


The  trapezium 
Perpend.  B  a 
—    Do 

Halfdiag.  AC 

Square  chains 

The  triangle 
Perpend.  E  n 
Half  side  A  F 

ABCD. 

11.68 
17.10 

The  triangle 
Half  perp.  E  m 
Diag.  A  D    - 

ADE. 
4.90 
35 

27.78 
22.50 

143900 
5756 
5756 

2450 
1470 

Square  chains    •         171.50 

Trap.  ABCD      -     647.55 
Triangle  A  DE     -     171.50 
Triangle  AFE     -     163.10 

Acres  98)215 
4 

Roods  .860 
40 

Rods  34)400 

-     647.5500 

AFE. 
11.65 
14 

4660 
1165 

Square  chains                  163.10 

Acres  Roods  Rods 
Area   98—0—34.4 

REMARKS. 

As  each  of  the  sides  of  the  several  triangles,  into  which  the 
preceding  plot  of  a  field  is  divided,  is  known  from  the  field- 
book,  the  area  of  the  field  may  be  calculated  arithmetically, 
by  finding  the  area  of  each  triangle,  according  to  PROS.  IX. 
Rule  3  ;  and  then  adding  the  whole  together.  This  method, 
though  it  may  require  more  time,  is  preferable  to  the  other, 
because  more  accurate.  Indeed  it  is  always  better  to  calcu- 
late the  area  of  a  field  arithmetically  than  geometrically, 
for  in  the  former  no  two  persons  can  differ  in  their  calcula- 
tions; whereas,  according  to  the  latter,  which  is  the  com- 
mon method  of  casting  the  contents  of  a  field,  it  is  hardly  to 
be  expected  that  any  two  persons  will  perfectly  agree.  The 
inaccuracy  of  scales,  and  the  difficulty  of  determining  with 
precision  the  length  of  sides  and  perpendiculars  with  a  scale 
and  dividers,  render  it  almost  if  not  quite  impossible  to  ob- 
tain the  exact  area  of  a  field,  in  the  method  commonly  prac- 
tised, even  if  the  surveyor  has  measured  it  accurately  in  thd 
first  place. 

5* 


50  SURVEYING. 

Other  methods  of  taking  the  survey  of  a  field  by  the  chain 
only,  are  mentioned  in  some  treatises  on  this  subject,  but  they 
are  rather  curious  than  useful ;  and  it  is  much  better  to  as- 
certain the  angles  by  an  accurate  compass,  or  some  instru- 
ment designed  purposely  for  taking  angles. 


CASE    IV. 
TO  SURVEY  A  FIELD  WITH  A  CHAIN  AND  COMPASS. 

Measure  the  length  of  the  sides  with  a  chain,  and  take 
their  bearing  or  course  with  a  compass;*  enter  these  in  a 
field-book ;  plot  the  field  on  paper,  and  calculate  the  area  by 
the  directions  already  given. 

TO  PROTRACT  OR  DRAW  A  MAP  OF  A  FIELD. 

Draw  a  line  to  represent  a  meridian,  or  north  and  south 
line,  from  which  lay  off  a  bearing  or  course  of  the  first  side 
of  the  fieM,  with  a  protractor,  or  from  a  line  of  chords;  and 
from  a  scale  of  equal  parts,  measure  the  length  of  the  side,  and 
draw  a  line  to  represent  it. 

At  the  end  of  this  line  draw  a  line  parallel  to  the  meridian 
Hne,  and  then  lay  off  the  second  side  of  the  field  as  before 
taught;  proceed  in.  the  same  manner  to  draw  parallel  lines, 
and  lay  off  the  several  sides  till  the  whole  is  protracted. 

In  protracting  a  field,  let  the  top  of  the  paper  be  considered 
as  north,  the  bottom  south,  the  right  hand  east,  and  the  left 
hand  west;  lay  the  course  to  the  right  or  left  of  the  meridian 
line,  according  as- it  is  oast  or  west,  and  upwards  or  down- 
wards, according  as  it  is  north  or  south. 

In  all  protractions,  if  the  end  of  the  last  distance  falls  ex- 
actly on  the  point  from  which  you  began,  the  course  also 
beiag  right,  the  fieki  work  and  protractions  are  truly  taken 
and  performed;  if  not,  an  error  must  have  been  committed 
in  one  of  them :  in  such  cases,  make  a  second  protraction ; 
if  this  agrees  with  the  former,  it  is  to  be  presumed  the  fault 
is  in  the  field  work  -  a  re-survey  must  then  be  taken. 

*  A  compass  may  be  so  constructed  with  two  indexes,  one  moveable 
and  the  other  fixed,  as  to  ascertain  the  angles  made  by  two  sides,  without 
reference  to  the  bearing  of  those  sides.  Such  a  compass  would  be  par- 
ticularly useful  in  surveying  land  where  there  are  mineral  substances 
•which  have  an  influence  upon  the  compass  needle,  attracting  it  one 
way  or  the  other,  and  thus  rendering  it  impossible  to  take  a  course  by 
it  with  precision. 


SURVEYING. 


51 


FIELD  BOOK.  See  Fig.  53. 


Fig.  53. 


Ch.  L. 

A 

B. 

N. 

7° 

0' 

w. 

28.20 

B 

B 

C. 

N 

74 

0 

E. 

39.50 

i  v 

C 

D. 

S. 

9 

0 

E. 

38. 

D 

E. 

N 

.  63 

20 

W. 

14.55 

I 

E 

A. 

S. 

74 

0 

W. 

28.60 

Acres 

Roods 

Rods 

Area  117—1—6 

A 

REMARKS. 

The  sides  of  the  several  triangles  into  which  the  plot  of  a 
field  is  divided  may  be  found  by  trigonometry ;  and  then  the 
area  of  each  triangle  may  be  calculated  according1  to  PROB. 
IX.'jRw/e  3.  The  sum  of  the  areas  of  the  several  triangles 
will  be  the  area  of  the  whole  field.  This  method  may  re- 
quire more  time,  but  it  is  perfectly  accurate,  since  no  de- 
pendence is  placed  on  the  uncertain  measurement  of  scale 
and  dividers. 

In  the  preceding  EXAMPLE,  suppose  the  field  divided  into 
three  triangles.  See  Fig.  53.  In  the  triangle  E  A  B,  the 
sides  E  A  and  A  B  are  known  from  the  FIELD  BOOK,  and  their 
contained  angle  is  known  from  the  bearing  of  the  sides. 
The  other  angles  and  the  side  EB  maybe  found  by  OBLIQUE 
TRIGONOMETRY,  CASE  III. ;  and  then  there  will  be  the  three 
sides  to  find  the  area.  In  the  triangle  E  B  C,  the  side  B  C  is 
known  from  the  FIELD  BOOK,  and  the  side  E  B  is  found  as 
above  mentioned  ;  the  angle  E  B  A  is  also  found  as  above  ; 
this  substracted  from  the  angle  ABC,  which  may  be  found 
from  the  bearing  of  the  sides  A  B  and  B  C,  will  leave  the  an- 
gle EBC;  there  will  then  be  the  two  sides  and  their  con- 
tained angle  to  find  the  third  side;  and  this  being  found, 
there  will  be  the  three  sides  to  find  the  area.  In  the  trian- 
gle E  D  C,  the  sides  DE  and  D  C  are  known  from  the  FIELD 
BOOK,  and  their  contained  angle  is  known  from  the  bearing 
of  the  sides. ,  The  side  E  C  and  the  area  may  be  found  as 
above. 

It  is  recommended  to  the  learner  to  make  these  calcula- 


52 


SURVEYING. 


tions,  as  it  will  improve  him  in  the  knowledge  of  trigonome- 
try. 

NOTE.    Two  sides  and  their  contained  angle  being  given,  the  area 
may  be  found  by  PROB.  IX.  Rule  4. 


ANOTHER  METHOD  OF  PROTRACTING  FIELDS. 

Without  drawing  parallel  lines  at  the  end  of  each  side,  a  field 
may  be  protracted  by  the  angles  made  by  the  several  sides; 
and  the  angle  made  between  any  two  sides  may  be  found  by 
the  following  RULES. 

RULE  1.  If  the  course  or  bearing  of  one  of  the  sides  is 
north  and  the  other  south,  one  east  and  the  other  west,  sub- 
stract  the  less  course  from  the  greater. 

RULE  2.  If  one  is  north  and  the  other  south,  and  both 
east  or  west,  add  both  courses  together. 

RULE  3.  If  both  are  north  or  south,  and  one  east  and  the 
other  west,  substract  their  sum  from  180°. 

RULE  4.  If  both  are  north  or  south,  and  both  east  or 
west,  add  the  less  course  to  the  supplement  of  the  greater. 

In  each  case,  the  result  will  give  the  angle  contained  by 
the  two  sides. 

To  protract  a  field  according  to  the  preceding  rules,  is 
preferable  to  the  method  of  doing  it  by  parallel  lines,  though 
it  may  not  be  so  easy  to  the  learner  at  first.  It  is  difficult 
to  draw  parallel  lines  with  perfect  accuracy,  and  a  small  de- 
viation from  a  true  line  may  make  considerable  difference  in 
the  plot  of  a  field.* 


EXAMPLE  II. 

FIELD  BOOK.     See  Fig.  54. 


AB. 
B  C: 
CD. 
DE. 
E  A. 


N. 


S. 

N. 


16° 

82 

17 

37 

49 


30' 
0 
0 
0 
0 


Ch.  L. 
E.  22. 
E.  19.60 

24. 

22. 

25.20 


E. 

W. 

W. 


Area  84  acres.  g! 

*  See  Appendix,  No.  7. 


SURVEYING. 


53 


TO  DRAW  A    PLOT  OF    THIS  FIELD,  ACCORDING  TO  THE  PRE- 
CEDING RULES. 

Having  drawn  the  side  AB,  according  to  the  directions  be- 
fore given  for  laying  off  the  first  course  and  distance,  com- 
pare the  first  and  second  courses  together,  and  they  will  be 
found  to  be  both  north  and  both  east ;  consequently,  the  an- 
gle between  them  is  found  by  RULE  4,  as  follows :  16°  30' 
the  less  course,  and  98°,  the  supplement  of  the  greater,  being 
added,  the  sum  is  114°  30',  for  the  angle  at  B.  Compare  the 
second  and  third  courses,  and  they  will  be  found  to  be  one 
north  and  one  south,  and  both  east ;  consequently,  according 
to  RULE  2,  82°,  the  second  course,  added  to  17P,  the  third 
course,  the  sum  99°,  is  the  angle  at  C.  The  third  and  fourth 
courses  are  both  south,  and  one  east  and  the  other  west. 
The  angle  between  them  at  D  is  126°;  for  17°,  the  third 
course  added  to  37°,  the  fourth  course,  is  54°,  which  substracted 
from  180°,  leaves  126°,  according  to  RULE  3.  The  fourth  and 
fifth  courses  are  one  south  and  the  other  north,  and  both 
west.  According  to  RULE  2,  27°,  the  fourth  course,  added  to 
49°,  the  fifth  course,  the  sum  86°,  is  the  angle  at  E. 

A  little  practice  will  render  this  mode  of  protracting  a  field 
familiar  and  easy,  and  an  attention  to  the  courses  will  show 
in  what  direction  the  angle  is  to  be  made. 


EXAMPLE    III. 

FIELD  BOOK.     See  Fig.  55. 


54 


SURVEYING. 


Ch.  L. 

AB. 

N. 

56° 

15' 

E. 

21.60 

BC. 

N. 

26 

30 

E. 

13.44 

CD. 

S. 

71 

30 

E. 

18.96 

DE. 

S. 

26 

30 

E. 

13.44 

EF. 

S. 

71 

30 

W. 

18.96 

FG. 

S. 

45 

0 

E. 

8.47 

GH. 

S. 

63 

30 

E. 

13.44 

H  I. 

N. 

45 

0 

E. 

8.47 

I  K. 

S. 

26 

30 

E. 

13.44 

KL. 

S. 

45 

0 

W. 

8.47 

LM. 

S. 

63 

30 

W. 

13.44 

MN. 

N. 

76 

0 

W. 

24.73 

N  A. 

N. 

36 

45 

W. 

30. 

Acres  Roods  Rods 
Area  167—1—30 


The  above  field  may  be  protracted,  and  its  area  calculated 
according  to  the  directions  given  in  the  preceding  EXAMPLES. 


SEVERAL  FIELD  BOOKS  TO  EXERCISE  THE  LEARNER  IN  PLOT- 
TING FIELDS  AND  CALCULATING  THEIR  AREA. 

Ch.  L. 

No.  I.             Rods     8.     N.  53°  15'    W.    11.60 

1. 

N.     15°  0'   E. 

320 

9. 

N. 

36     45     E.     19.20 

2. 

N.     37  30     E. 

160 

10. 

N. 

22     30     E.      14. 

3. 

East 

120 

11. 

S. 

76     45     E.      12. 

4. 

S.      11     0      E. 

200 

12. 

S. 

15       0     W.    10.85 

5. 

South 

216 

13. 

S. 

16     45     W.    10.12 

6. 

West 

160 

Acres  Roods  Rods. 

7. 

S.      36  30     W. 

160 

Area  110—2—23 

8. 

N.     38  15     W. 

136 



Acres  Roods  Rods. 

No.  III.           Rods 

Area  744—3—28 

1. 

S. 

65°  40'    W.       49.7 

__ 

2. 

S. 

67     15     W.       34.5 

No.  II. 

Ch.  L. 

3. 

S. 

54       0     W.       17.9 

1. 

N.     75°  0'    E. 

13.70 

4. 

S. 

20       0     W.         5.8 

2. 

N.     20  30     E. 

10.30 

5. 

S. 

7     30     E.        29.4 

3. 

East 

16.20 

6. 

N. 

83       0     E.       107.4 

4. 

S.     33  30     W. 

35.30 

7. 

N. 

5     50     W.       22. 

5. 

S.     76     0     W. 

16. 

8. 

N. 

18     30     W.      46. 

6. 

North 

9. 

Acres  Roods  Rods. 

7. 

S.     84    0     W. 

11.60 

Area  34—1—19 

SURVEYING. 


55 


No.  IV.        Rods. 

Rods. 

1.     N.     43°  0'    W.    12.44 

10.     N.     64°  0'     E.       12.5 

2.     N.     64     0     W.      8. 

11.     N.     49     0     E.       14. 

3.     N.     52     0     W.     14.60 

12.     N.     26   10     W.      19.3 

4.     N.     37     5     W.    51.36 

13.     N.     21     0     W.      18.3 

5.     N.     15  30     W.    21.76 

14.     N.     44  10     W.      18. 

6.     N.     20  40     W.    44.60 

15.     N.     64  40     E.        30.5 

7.     N.     88  20     E.    167.60 

16.     N.     18  30     W.      39. 

8.     S.      34  40     E.      71.20 

17.     N.     86     5     E.       26.7 

9.     S.      75     0     W.    69.72 

Acres  Roods  Rods. 

10.     S.      55     0     W.    64.60 

Area  48—1  —  12 

11.     S.      25     0     W.     18.12 

Acres  Roods  Rods. 

No.  VII.     Ch.  L. 

Area  97  —  2  —  29 

1.     N.       0°  45'    W.    9. 

2.     N.     19     30     W.    5.35 

No.  V.         Rods. 

3.     N.     23       0     W.    4.09 

1.     S.     11°  50'    W.     34.6 

4.     N.     41     35     W.    6.15 

2.     S.     63     20     E.       93.6 

5.     N.       3       0     W.  36.75 

3.     N.      4       0     W.      34.9 

6.     S.      86     50     W.  13.33 

4.     S.     89     55     E.       40.1 

7.     N.       2     15     W.  17.65 

5.     N.      5     20     W.     35.5 

8.     N.     85     45     E.    12.56 

6.     N.    69     40     W.     60. 

9.     S.        2     10     E.      8. 

7.     S.     78       0     W.     30.6 

10.     N.     86     45     E.      7.38 

8.     N.    67     20     W,        1.2 

11.     S.        3     15     E.    13.20 

9.     S     72     30     W.      10.4 

12.     N.     87       0     E.  29.92 

10.     S.    66     55     W.      15.2 

13.     N.     49     20     E.     4.04 

Acres  Roods  Rods. 

14.     North                        2.23 

Area  41  —  1  —  34 

15.     N.     50     35     E.      6.50 



16.     S.      22     50     E.    17.94 

No.  VI.       Rods. 

17.     S.      34       0     W,    3.50 

1.     S.     34°     0'    E.       42.8 

18.     S.      41       0     W.    3. 

2.     S.     29       0     E.       69.4 

19.     S.      22     50     W.    9.25 

3.     S.     64     50     W.     53. 

20.     S.        3     40     E.      2.64 

4.     S.     25       0     E.         4. 

21.     S.      86       0     W.    2.50 

5.     S.     66     30     W.     39. 

22.     S.        0     25     W,  14.50 

6.     N.    25       0     W.       4. 

23.     S.        2       0     W.    5.38 

7.     S.     64     45     W.     32.2 

24.     S.      10       0     E.    11.75 

8.     N.    30     30     W.     18.3 

25.     S.      86       0     W.  34.60 

9.     N.    56     30     E.      34.5 

Acres  Roods  Rods. 

Area  268  —  3  —  7 

CASE    V. 

TO    SURVEY  A    FIELD    FROM     ONE    STATION    AT   ANY    PLACE 


56 


SURVEYING. 


WITHIN  THE  FIELD,   FROM  WHICH  THE   SEVERAL  ANGLES 
MAY  BE  SEEN. 

Take  the  bearing  of  the  angles,  and  measure  their  distance 
from  the  station. 


FIELD  BOOK.     See  Fig.  56. 


Fig.  56. 


From  station  to  A.  N.  20°  W. 

B.  N.  60  E. 

C.  N.  87  E. 

D.  S.  15  E. 

E.  S.  60  W. 

F.  N.  65  W. 


TO  PROTRACT   THIS  FIELD. 


Draw  a  meridian  line  as  N.  S.  From  some  point  in  that 
line  as  a  centre,  lay  off  the  bearing"  and  distance  to  the  sev- 
eral angles,  and  draw  lines  from  one  angle  to  another,  as 
AB,  BC,  CD,  &c. 


TO  FIND  THE  AREA. 

The  area  may  be  calculated  according  to  PROS.  XII.  by 
measuring  diagonals  and  perpendiculars  ;  or  more  accurately 
according  to  PROB.  IX.  RuJe  4. 

As  the  bearing  and  distance  of  the  lines  from  the  station  to 
the  several  angles  are  known,  two  sides  and  their  contained 
angle  are  given  in  each  of  the  triangles  into  which  the  plot 
is  divided ;  the  area  may,  therefore,  be  readily  calculated  by 
the  RULE  above  referred  to. 

NOTE.  As  in  the  operation,  the  logarithm  of  radius  is  to  be  substract- 
ed  from  the  sum  of  the  other  logarithms,  it  may  be  done  by  re- 
jecting the  left  hand  figure,  without  the  trouble  of  putting  down 
the  ciphers  and  substracting. 


SURVEYING. 


57 


Triangle  a  A  B. 
a  A,  8.70    -    -    -    0.939519 


aB,  10       -    - 
Sine  A  a  B,  80° 


1.000000 
9.993351 


Doub.  area,  85.67  -     1 .932870 


Triangle  a  B  C. 
aB,  10        ...     1.000000 


aC,  11.40  -    - 
Sine  B  a  C,  27° 


1.056905 
9.657047 


Doub.  area,  51.75  -    1.713952 


Triangle  a  C  D. 
aC,  11.40  -     -     -     1.056905 
aD,  10.50  -     -     -     1021189 
Sine  C.a  D,  78°   -     9.990404 


Doub.  area,     117  -  2.068498 


Triangle  a  D  E. 
aD,  10.50    -    -     -  1.021189 
a  E,  12         ...  1.079181 
Sine  D  a  E,  75°      -  9.984944 


Doub.  area,  121.7  -  2.085314 


Triangle  a  E  F. 
aE,  12         -    -     -  1.079181 


aF,    8.78     -    - 
Sine  E  a  F.  55° 


-  0.943495 

-  9.913365 


Doub.  area,  86.31  -  1.936041 


a  F,  8.78 
a  A,  8.70 


Triangle  a  F  A. 


-  0.943495 

-  0.939519 


Sine  F  a  A,  45°     -  9.849485 


Doub.  area,  54.01  -  1.732499 


Triangle  a  A  B 
aBC 
aCD 
aDE 
aE  F 
aF  A 

Double  area 
Area    • 


-     516.54 
.    25)827 


827 
4 

3)308 
40 

12)320 

Acres  Roods   Rods. 
•Area  25  —  3—12.32 


CASE    VI. 


TO  SURVEY  A  FIELD  FROM  SOME  ONE  OF  THE  ANGLES,  FROM 
WHICH  THE  OTHERS  MAY  BE  SEEN. 


From  the  stationary  angle,  take  the  bearing  and  distance 
to  each  of  the  other  angles,  with  a  compass  and  chain. 
6 


58  SURVEYING. 

FIELD  BOOK.     See  Fig.  57. 


Fig.  57. 


FG. 
FA. 
FB. 
FC. 
FD. 
FE. 


N. 
N. 
N. 
N. 
N. 
N. 


70° 
50 
30 
10 
7 
30 


W. 

w. 
w. 
w. 

E. 
E. 


Ch.  L. 
14.60 
18.20 
16.80 
21.20 
16.95 
8.50 


TO  DRAW  A  PLOT  OF  THIS  FIELD. 

Draw  a  meridian  line  to  pass  through  the  stationary  angle 
as  at  F.  From  the  point  F,  lay  off  the  bearing  and  distance 
to  the  several  angles,  and  connect  them  by  lines,  as  F  G,  F  A, 
FB,  &c. 

The  area  may  be  calculated  as  taught  in  the  preceding 

CASE. 


CASE     VII. 


TO  SURVEY  A  FIELD  FROM  TWO  STATIONS  WITHIN  THE 
FIELD,  PROVIDED  THE  SEVERAL  ANGLES  CAN  BE  SEEN 
FROM  EACH  STATION. 

Find  the  bearing  from  each  station  to  the  respective  an- 
gles; and  also  the  bearing  and  distance  from  one  station  to 
the  other. 


SURVEYING. 

FIELD  BOOK.     See  Fig.  58. 


59 


First  Station. 
AC.     N.     38°  30'    E. 


A  D.  S.      69 

A  E.  S.      59 

AF.  N.     63 

AG.  N.     21 
A  H.  North. 


0  E. 

0  W. 

0  W. 

0  W. 


Second  Station. 

BC.  S.     82°  0'    E. 

BD.  S.     17     0     E. 
B  E.     S.     28     0     W. 


B  F.     S. 
BG.     N.    76 
BH.     N.   24 


49  0  W. 
0  W. 
0  W. 


Stationary  line  A  B.  N.  14°  E.  20  chains. 


TO  PROTRACT  THIS  TIELD. 

At  the  first  station  A,  draw  a  meridian  line,  and  lay  off  the 
bearings  t9  the  respective  angles;  draw  the  stationary  line 
A  B,  according  to  the  bearing  and  distance ;  at  B  draw  a 
meridian  line  parallel  to  the  other,  and  lay  off  the  bearings 
to  the  angles,  as  taken  from  this  station ;  from  each  station 
draw  lines  through  the  degree  which  shows  the  bearing  of 
each  angle,  as  marked  by  the  protractor  or  line  of  chords, 
and  the  points  where  those  lines  intersect  each  other  will  be 
the  angles  of  the  field.  Connect  those  angular  points  to- 
gether by  lines,  and  those  lines  will  represent  the  several 
sides  of  the  field. 


CASE    VIII. 

,  TO  SURREY  AN  INACCESSIBLE  FIELD. 

Fix  upon  two  stations  at  a  convenient  distance  from  the 


60 


SURVEYING. 


field,  from  each  of  which  the  several  angles  maybe  seen; 
from  each  station  take  the  bearing  of  the  angles ;  and  take 
the  bearing  and  distance  from  one  station  to  the  other.* 

FIELD  BOOK.     See  Fig.  59.  Fig.  59. 


First  Station. 


AE. 
AF. 
AG. 
AD. 
AH. 
AC. 

N. 
N. 

N. 
N. 

N. 
N. 

9° 
16 
14 
39 
40 
72 

15' 
0 
30 
0 
0 
0 

E. 
E. 
E. 
E. 
E. 
E. 

N 

s 

^    . 

A 

1--  1 

-••"*" 

XC 

/C 

«*, 

si 

£4 

B 

Second  Station. 

BE. 

N. 

50°  0'    W. 

B  F. 

N. 

29   15     W. 

B  D. 

N. 

24     0     W. 

BG. 

N. 

21   30-   W. 

BH. 

N. 

5     0     E. 

B  C. 

N. 

20  30    E. 

Ch. 

L. 

Stationary  distance  A  B.  S.  88°  30'  E.  19.20. 

44. 

The  directions  given  in  the  last  CASE  for  plotting  the  field, 
will  apply  in  this  CASE  also  ;  and  the  area  in  this  and  the  pre- 
ceding CASE  may  be  calculated  in  the  manner  pointed  out  in 
CASE  IV.  by  dividing  the  plot  into  triangles,  and  measuring 
diagonals  and  perpendiculars.  Or  the  sides  may  be  found 
by  trigonometry,  and  the  area  calculated  arithmetically,  as 
already  taught. 


CASE   IX. 

TO    SURVEY  A    FIELD    WHERE   THE    BOUNDARY    LINES    ARE 

*  This  method  of  practice  is  subject  to  much  error. 


SURVEYING. 


51 


VERY  IRREGULAR,  WITHOUT  NOTICING  WITH  THE  COMPASS 
EVERY  SMALL  BEND. 


Begin  near  one  corner  of 
the  field,  as  at  A,  Fig.  60, 
and  measure  to  the  next 
large  corner,  as  B,  in  a 
straight  line  ;  noticing  also 
the  bearing  of  this  line. 
From  the  line  take  offsets 
to  the  several  bends,  at  right 
angles  from  the  line;  noti- 
cing in  the  FIELD  BOOK  at 
what  part  of  the  line  they  are 
taken,  as  at  A1,H2,I3,  B4. 
Proceed  in  the  same  manner 
round  the  field.  Inthe  figure, 
the  dotted  lines  represent 
the  stationary  lines,  and  the 
black  lines  the  boundaries  of 
the  field. 


Fig.  60. 


Bearing  and  Distance. 

Offsets. 

Bearing  and  Distance. 

Offsets. 

Ch.  L. 
AB.  N.  85°0/E.  11.20 
at  5.40 

8.26 
the  end 

Ch.  L. 
0.56 
1.40 
0.36 
0.36 

Ch.  L. 
E  F.  S.67°  50'  W.  8.20 
at  1.04 
2.96 

5.88 
the  end 

Ch.  L. 
0.40 
0.36 
0.33 
1. 
0.12 

B  C.  N.  7°  20'  >,.    7  96 
at  2.36 
4.28 
1   e  end 

0.20 
0.36 
0.96 
0.30 

F  G.  S.  27°  40'  E.   7  06 
at  2. 
the  end 

1.20 
0.24 
016 

CD.  N.  62°  0'  W    4.6b 
at  4  34 

0.30 
030 

GA.  S.^WW.  6.48 
at  3.80 
the  end 

0.80 
0.40 

DE.  N.I  PUT  W.  4.20 

TO  PROTRACT  THIS  FIELD. 

Draw  the  stationary  lines  according  to  the  directions  in 
CASE  IV.  From  A  make  an  offset  of  56  links  to  I ;  measure 
from  A  to  H  540  links,  and  make  the  offset,  H  2,  140  links; 
measure  from  A  to  I  826  links,  and  make  the  offset  I  3,  36 
links ;  at  B  make  the  offset  B  4,  36  links.  Proceed  in  the 
same  manner  round  the  field,  and  connect  the  ends  of  the  off- 
sets  by  links,  which  will  represent  the  boundaries  of  the  field. 


62  SURVEYING. 


TO  FIND  THE  AREA. 

Find  the  area  within  the  stationary  lines  as  before  taught  j 
then  of  the  several  small  trapezoids,  rectangles,  and  trian- 
gles, made  by  the  stationary  lines,  offsets,  and  boundary  lines, 
and  add  the  whole  together  :  thus,  add  56  links,  the  offset  A 
1,  to  140  links,  the  offset  H  2,  and  multiply  their  sum,  196,  by 
half  540,  the  length  of  the  line  A  H,  and  the  product  52920 
square  links,  will  be  the  area  of  thetrapezoid  A  H  21  ;  again, 
add  140,  the  offset  H  2,  to  36,  the  offset  I  3,  and  multiply  their 
sum,  176,  by  half  286,  the  length  of  the  line  H  I,  and  the  pro- 
duct, 25168  square  links,  will  be  the  area  of  the  trapezoid 
H  I  3  2.  Proceed  in  the  same  manner  to  calculate  the  area 
of  all  the  trapezoids,  triangles,  &c. 


CASE    X. 

TO  SURVEY  A  FIELD  BY  TAKING  OFFSETS  BOTH  TO  THE  RIGHT 

AND  LEFT;  THAT  is,  WITHIN  AND  WITHOUT  THE  FIELD, 

AS  OCCASION  SHALL  REQUIRE,  IN  CONSEQUENCE  OF  THE 
STATIONARY  LINES  CROSSING  THE  BOUNDARY  LINES J 
ALSO,  BY  INTERSECTIONS,  THAT  IS,  TAKING  THE  BEARING 
OF  AN  INACCESSIBLE  CORNER  FROM  TWO  STATIONS."  - 

The  directions  given  in  the  preceding  CASE,  together  with 
the  following  FIELD  BOOK,  will  show  the  learner  how  to  sur- 
vey a  field  like  the  following,  and  also  to  protract  it  when 
surveyed. 


SURVEYING. 

FIELD  BOOK.     See  Fig.  61. 


Fig&l. 


Offsets, 
to  the 
Left. 

Bearing  and  distance. 

Offsets, 
to  the 
Right. 

Remarks. 

Ch.  L. 
1.12 
3.40 
1.25 

Ch.  L. 
AB.  N.  88°0'W.      22.12 
at  4.25 
7.40 
13. 

Ch.  L. 

A  tower  bears  from 
A.  N.  48°  W. 

1.45 

B  C.  N.  27°  45'  W.    21.12 
at  4  10 
10.25 
15. 

1.20 
1.15 

From  B  the  tower  bears 
N.  38°  30'  E. 

01.  S.    82°15/E.         5.45 
1  2  N.    70      0  E.      13.25 
2  D.  N.  20      0  E.        3.36 

From  C  go  into  the  field 
to  1,  on  account  of  some 
impediment  on  or  near 
the  boundary  line.  AtD, 
you  get  into  another  cor- 
ner of  the  field. 

D  P.  S.  35°  0'  E.       15.15 

E.  an  inaccessible  cor- 
ner, bears  from.  D.  S. 
65°  30'  E. 

2.20 
2.32 

FA.  S.  15°  15'  E.      15.10 
at  1.20 
7.45 
12.25 

1.36 

E.  the  inaccessible  corner, 
bears  from  F.  N.  4°  W. 

NOTE. — To  draw  a  tree,  house,  tower,  or  any  other  remarkable  ob- 
ject, in  its  proper  place,  in  the  plot  of  a  field — from  any  two  stations, 
while  surveying  the  field,  take  the  bearing  of  an  object,  and  the 
intersection  of  the  lines,  which  represent  the  bearings,  will  deter- 
mine the  place  of  the  object,  in  the  same  manner  that  the  tower  is 
drawn  in  ihe  figure. 


64  SURVEYING. 


TO  FIND  THE  AREA  OF  THE  ABOVE  FIELD. 

Find  the  area  within  the  stationary  lines,  and  then  of  the 
several  small  trapezoids,  &c.  remembering1  to  distinguish 
those  without  the  stationary  lines  from  those  which  are  with- 
in. Substract  the  area  of  those  within  the  stationary  lines 
from  the  area  of  those  without,  and  add  the  remainder  to  the 
area  contained  within  the  stationary  lines ;  the  sum  will  be 
the  whole  area  of  the  field. 

[Or,  add  the  areas  of  those  without  the  stationary  lines,  to 
the  area  contained  within  those  lines,  and  substract  from  the 
sum  the  areas  of  the  several  triangles,  trapezoids,  &c.  with- 
in the  stationary  lines.] 


SECTION    III. 

RECTANGULAR  SURVEYING,  OR  AN  ACCURATE  METHOD  OF 
CALCULATING  THE  AREA  OF  A  FIELD  ARITHMETICALLY,  FROM 
THE  FIELD  BOOJC,  WITHOUT  THE  NECESSITY  OF  PROTRACTING 
IT,  AND  MEASURING  WITH  A  SCALE  AND  DIVIDERS,  AS  IS 
COMMONLY  PRACTISED. 

I.  Survey  the  field  in  the  usual  method,  with  an  accurate 
compass  and  chain,  and  from  the  field  book  set  down,  in  a 
traverse  table,  the  course  or  bearing  of  the  several  sides,  and 
their  length  in  chains  and  links,  or  rods  and  decimal  parts  of 
a  rod ;  as  in  the  2nd  and  3d  columns  of  the  following  EX- 
AMPLE. 


SURVEYING. 


65 


EXAMPLE  I. 

II 

i 
i 

i 
i 

1 
1 
1 

1 

91fi6.7040 

ci 

1 
1 
1 

i 

I 

§ 

co' 

w 

s 

11 

1600.0910 

1 

1 

I 
l 
I 

1 

1 

1 

(L,^ 
c* 

1 

S 

1 

1 

ffi 

§ 

g 

P 

5* 



l§ 

i 

J_ 

i- 

TT 

i'- 

oS 

i 

{: 

5 

°"¥" 

oci 

55 

o 
o 

H 

i 

11 

II 

11 

cioi 

| 

y 

o  ^ 

02 

I 

i 
i 

11 

00 

• 

^  s 

CO  t5 

* 

~H    r-J 

\ 

, 

1 

; 

1 

o           QO 

§     s     s 

o 

§ 

i 

js 

1 
O 

N.  15°  0'  E. 

H 

w 

w 

o 
oi 

1 

« 

s 

c^ 

No. 

'H 

<M 

CO 

>* 

»rj 

to 

^ 

00 

19143.9019  sum  of  South  Areas. 
4245.4016               North     do. 

2)14898.5003 

Acres  744)92501 
4 

Roods  3)70004 
40 

Rods  28)00160 

Acres  Roods  Rods 
Area  7 44  —  3—  28 


66  SURVEYING. 

2.  Calculate  by  RIGHT  ANGLED  TRIGONOMETRY,  CASK  I, 

or  find  by  the  table  of  difference  of  latitude  and  departure,* 
or  by  the  table  of  natural  sines,f  the  northing  or  southing, 
easting  or  westing,  made  on  each  course,  and  set  them  down 
against  their  several  courses  in  their  proper  columns,  marked 
N.  S.  E.  W. 

NOTE.  To  determine  whether  the  latitude  and  departure  for  any 
particular  course  and  distance  are  accurately  calculated,  square 
each  of  them  ;  and  if  they  are  right,  the  sum  of  their  squares  will 
equal  the  square  of  the  distance,  for  the  following  reason:  the  la- 
titude and  departure  represent  the  two  legs  of  a  right  angled  tri- 
angle, and  the  distance  the  hypothenuse;  and  it  is  a  mathematical 
truih,  that  the  square  of  the  hypothenuse  of  any  right  angled  tri- 
angle, is  equal  io  the  sum  of  the  squares  of  the  two  legs. 

3.  If  the  survey  has  been  accurately  taken,  the  sum  of  the 
northings  will  equal  that  of  the  southings,  and  the  sum  of  the 
eastings  will  equal  that  of  the  westings.     If,  upon  adding  up 
the  respective  columns,  these  are  found  to  differ  very  con- 
siderably, the  field  should  be  again  surveyed;  as  some  error 
must  have  been  committed,  either  in  taking  the  courses,  or 
measuring  the  sides.     If  the  difference  is  smafl,  a  judicious, 
experienced  surveyor,  will  judge   from   the   nature   of   the 
ground,  or  shape  of  the  field  surveyed,  where  the  mistake 
was  most  probably  made,  and  will  correct  accordingly.     Or, 
the  northings  and  southings,  and  the  eastings  and  westings, 
may  be  equalled  by  balancing  them,  as  follows :    substract 
one  half  the  difference  from  that  column  which  is  the  largest, 
and  add  it  to  that  column  which  is  the  smallest;  and  let  the 
difference,  to  be  added  or  substracted,  be  divided  among  the 
several  courses,  according  to  their  length. 

In  EXAMPLE  I.,  the  upper  numbers  are  the  northings,  &c., 
as  found  by  a  table  of  difference  of  latitude  and  departure. 
The  several  columns  being  added,  the  northings  are  found  to 
exceed  the  southings  47  links,  and  the  westings  to  exceed 
the  eastings  24  links;  [47  being  uneven,  drop  a  link  from, 
the  northings,  and  it  becomes  46.  Let  half  of  this  (23)  be 
taken  from  the  northings,  and  added  to  the  southings ;]  like- 
wise, take  12  links  from  the  westings,  and  add  it  to  the  east- 
ings. Take  from  the  first  course  of  the  northings  12  links, 
from  the  second  7,  and  from  the  third  5 ;  to  the  first  southing 
add  7  links,  to  the  second  10,  and  to  the  third  6 ;  add  to  the 
first  easting  3  links,  to  the  second  3,  to,the  third  4,  and  to  the 

*  For  an  explanation  of  this  table,  and  the  manner  of  using  it,  see 
the  remarks  preceding  the  table. 
t  See  the  remarks  preceding  the  table  of  natural  sines. 


SURVEYING.  67 

fourth  2 ;  take  fronvthe  first  westing  5  links,  from  the  second 
4,  and  from  the  third  3.  [These  are  the  proportional  correc- 
tions belonging  to  each,  as  found  by  calculation.*]  The 
lower  numbers  will  then  represent  the  northings,  &c.  as 
balanced. 

4.  These  columns  being  balanced,  proceed  to  form  a  de- 
parture column,  or  a  column  of  meridian  distances;  which 
shows  how  far  the  end  of  each  side  of  the  field  is  east  or 
west  of  the  station  where  the  calculation  begins.     This  col- 
umn is  formed  by  a  continual  addition  of  the  eastings,  and 
substraction  of  the  westings ;  or  by  adding  the  westings  and 
substracting  the  eastings:  see  EXAMPLE  1. 

The  first  easting,  20.74,  is  set  for  the  first  number  in  the 
departure  column;  to  this  add  24.38,  the  second  easting, 
and  it  makes  45.12,  for  the  second  number;  to  this  add 
30.04,  the  third  easting,  and  it  makes  75.16,  for  the  third 
number ;  to  this  add  9.56,  the  fourth  easting,  and  it  makes 
84.72,  for  the  fourth  number ;  the  fifth  course  being  south, 
it  is  evident  the  meridian  distance  will  remain  the  same, 
therefore  place  against  it  the  same  easting  as  for  the  prece- 
ding course;  from  this  substract  39.95,  the  first  westing,  and 
it  leaves  44.77,  for  the  sixth  course ;  from  this  substract 
23.75,  the  second  westing,  and  it  leaver  21.02,  for  the  sev- 
enth course;  from  this  substract  21.02,  the  last  westing,  and 
it  leaves  0.0  to  be  set  against  the  last  course,  which  shows 
that  the  additions  and  substractions  have  been  accurately 
made.  For  as  the  eastings  and  westings  equal  each  other, 
it  is  evident  that  the  one  being  added  and  the  other  substract- 
ed,  there  will  be  in  the  end  no  remainder. 

5.  The  next  step  in  the  process  is  to  form  a  second  de- 
parture column,  the  numbers  in  which  show  the  sum  of  the 
meridian  distances  at  the  end  of  the  first  and  second,  second 
and  third,  third  and  fourth  courses,  &c. 

The  first  number  in  this  column  will  be  the  first  in  the 
other  departure  column ;  to  which  add  the  second  number  in 
that  column  for  the  second  in  this ;  for  the  third  add  the  se- 
cond and  third;  and  for  the  fourth  the  third  and  fourth ;  and 
so  on,  until  the  column  be  completed.  See  EXAMPLE  I. 

The  first  number  to  be  placed  in  the  second  departure  col- 
umn is  20.74;  to  this  add  45.12,  and  it  makes  65.86  for  the 
second  number  ;  to  45.12  add  75.16,  and  it  makes  120.28,  for 
the  third  number;  to  75.16  add  84.72,  and  it  makes  159.88 
for  the  fourth  number;  to  84.72  add  84.72,  and  it  makes 
169.44  for  the  fifth  number;  to  84.72,  add  44.77,  and  it  makes 

*  See  Appendix,  No.  5. 


63 


SURVEYING. 


129.49  for  the  sixth  number,  to  44.77  add  21.02,  and  it 
makes  65.79  for  the  seventh  number;  to  21.02  add  0.0, 
and  it  makes  21.02  for  the  eighth  number. 

6.  When  the  work  is  thus  far  prepared,  multiply  the 
several  numbers  in  the  second  departure  column  by  the 
northings  or  southings  standing  against  them  respectively; 
place  the  products  of  those  multiplied  by  the  northings  in 
the  column  of  north  areas,  and  of  those  multiplied  by  the 
southings  in  the  column  of  south  areas ;  add  up  these  two 
columns,  and  substract  the  less  from  the  greater ;  the  remain- 
der will  be  double  the  area  of  the  field  in  square  rods  or 
square  chains  and  links,  which  ever  measure  was  used  in  the 
survey. 

[In  the  preceding  explanations,  the  meridian  is  supposed 
to  pass  through  the  extreme  west  angle  of  the  field.  It  is 
best  always  to  take  the  extreme  east  or  west  angle.] 

Fig.  62. 


Demonstration  of  the  preceding  rules. 
See  Fig.  62.  and  EXAMPLE  I. 


The  dotted  line  A  2  represents  the  northing,  and  the  line 
2  B  the  easting,  made  by  the  first  course;  these  multiplied 
together,  that  is,  77.15x20.74=1600.0910,  which  is  double 
the  area  of  the  triangle  A  2  B,  as  is  evident  from  the  rule  to 
find  the  area  of  the  triangle,  PROB  IX.  Rule  I.  This  num- 
ber is  to  be  placed  for  the  first  number  in  the  column  of 
north  areas.  The  line  3  C  represents  the  sum  of  the  eastings 
made  by  the  first  and  second  courses,  which  is  45.12,  the  se- 
cond number  in  the  first  departure  column;  if  to  this  you 
add  20.74,  the  length  of  the  line  2  B,  you  have  65.86,  which  is 
the  second  number  in  the  second  departure  column,  and 
which  represents  the  sum  of  the  two  lines  3  C  and  2  B. 
These  two  lines,  with  the  line  2  3,  which  represents  the 


SURVEYING.  69 

f 

northing  made  by  the  second  course,  and  the  line  B  C,  one 
of  the  sides  of  the  field,  form  a  right  angled  trapezoid. 
Now,  by  the  rule  to  find  the  area  of  such  a  trapezoid,  see 
PROB.  X.,  65.86X31.66=2085.1276,  double  the  area  of  the 
trapezoid  2  B  C  3.  Place  this  product  for  the  second  number 
in  the  column  of  north  areas. 

To  the  line  3  C  add  C  D  30.04,  that  easting'made  by  the 
third  course,  and  you  have  75.16,  which  is  the  sum  of  the 
eastings  made  by  the  three  first  courses,  and  the  third  num- 
ber in  the  first  departure  column.  To  this  add  9.56,  the 
easting  of  the  fourth  course,  and  you  have  84.72,  the  length 
of  the  line  1  E,  which  represents  the  sum  of  the  eastings 
made  by  the  four  first  courses,  and  is  the  fourth  number  in 
the  first  departure  column.  These  two,  viz.,  the  lines  3D 
75.16,  and  i  E  84.72,  added  together,  make  159. 88,  the  fourth 
number  Jn  the  second  departure  column ;  which  being  multi- 
plied by  49.15,  the  length  of  the  line  3  1,  which  represents 
the  southing  made  by  the  fourth  course,  will  give  double 
the  area  of  the  trapezoid  1  E  D3.  The  number  thus  pro- 
duced is  7858.1020,  which  is  to  be  placed  for  the  first  num- 
ber in  the  column  of  south  areas. 

Tha  fifth  course  being  due  south,  it  is  evident  the  sum  of 
the  eastings  will  remain  the  same  as  at  the  end  of  the  fourth 
course;  that  is,  the  line  4F  equals  the  line  IE,  which  is 
84.72.  These  added,  make  169.44,  the  fifth  number  in  the  se- 
cond departure  column.  This,  being  multiplied  by  54.10,  the 
length  of  the  line  E  F,  which  is  the  southing  of  the  fifth 
course  as  corrected  in  balancing,  and  the  same  as  the  line  1 
4,  will  give  double  the  area  of  the  parallelogram  1  E  F4, 
which  is  9166.7040,  the  second  number  in  the  column  of 
south  areas. 

From  the  line  4  F  84.72,  substract  39.95,  which  is  a  west 
course  and  it  leaves  4  G  44.77,  the  sum  of  the  eastings,  or 
the  meridian  distance,  at  the  end  of  the  sixth  course,  and 
the  sixth  number  in  the  first  departure  column.  From  this 
substract  23.75,  the  westing  made  by  the  7th  course,  and  you 
have  21.02,  the  length  of  the  line  5  H,  which  is  the  meridian 
distance  at  the  end  of  the  seventh  course,  and  the  seventh 
number  in  the  first  departure  column.  The  line  4  G  44.77, 
added  to  the  line  5  H  21.02,  make  65.79,  the  seventh  number 
in  the  second  departure  column.  This  being  multiplied  by 
32.21,  the  length  of  the  line  4  5,  which  is  the  southing  of  the 
seventh  course,  will  give  double  the  area  of  the  trapezoid 
4  G  H  5,  which  is  21 19.0959,  the  third  number  in  the  column 
of  south  areas. 

The  line  H  5,  21.02,  is  the  westing  of  the  last  course,  and 
7 


70  SURVEYING. 

the  last  number  in'the  second  departure  column.  This  being 
multiplied  by  26.65,  length  of  the  line  5  A,  and  the  northing 
of  the  last  course,  produces  560.1830,  which  is  double  the 
area  of  the  triangle  A  5  H,  and  the  last  number  in  the  col- 
umn of  north  areas. 

NOTE.  It  will  be  observed  that  against  the  third  and  sixth  courses  there 
are  no  areas  ;  the  reason  is,  that  these  courses  being  one  east  and 
the  other  west,  there  is  no  northing  or  southing  to  be  multiplied 
into  them ;  regard  can  therefore  be  had  to  them  only  in  forming 
the  departure  columns. 

By  inspecting  the  figure,  and  attending  to  the  preceding 
illustrations,  it  will  be  seen  that  the  three  north  areas  repre- 
sent double  the  area  of  the  triangle  A  2  B,  the  trapezoid  2  B  C  3, 
and  the  triangle  A  5  H,  all  of  which  are  without  the  boun- 
dary lines  of  the  field  :  also,  that  the  three  south  areas  rep- 
resent double  the  area  of  the  trapezoid  3  DE  1,  the  parallelo- 
gram 1  E  F  4,  and  the  trapezoid  4  G  H  5  ;  and  that  these  in- 
clude not  only  the  field,  but  also  what  was  included  in  the 
north  areas.  Therefore  the  north  areas  substracted  from  the 
south,  the  remainder  will  be  double  the  area  of  the  field,  con- 
tained within  the  black  lines. 


ADDITIONAL  DIRECTIONS  AND  EXPLANATIONS. 

The  northings  and  southings  may  be  added  and  substract- 
ed instead  of  the  eastings  and  westings ;  then  there  will  be 
two  latitude  columns  instead  of  departure  columns,  and  the 
numbers  in  the  second  latitude  column  must  be  multiplied 
into  the  eastings  and  westings,  and  you  will  have  east  and 
west  areas. 

When  the  course  is  directly  north  and  south,  the  distance 
must  be  set  in  the  north  or  south  column ;  when  east  or  west, 
in  the  east  or  wesfcolumn.  There  will  therefore  sometimes 
be  no  number  to  be  added  to  or  substracted  from  the  num- 
ber last  set  in  the  latitude  or  departure  column ;  then  the 
number  last  placed  in  the  column  must  be  brought  down 
and  set  against  such  course ;  as  in  EXAMPLE  I.  at  the  5th 
course.  It  may  also  sometimes  be  the  case,  that  there  will 
be  no  number  to  multiply  into  the  number  in  the  second 
latitude  or  departure  column;  then  that  number  must  be 
omitted,  and  against  such  course  there  will  be  no  area,  as 
in  EXAMPLE  I.  at  the  3d  and  6th  courses. 

When  the  northings  or  southings,  eastings  or  westings, 
beginning  at  the  top,  will  not  admit  of  a  continual  addition 
of  the  one  and  the  substraction  of  the  other,  without  run- 


SURVEYING!. 


71 


ning  out  before  you  get  through  the  several  courses,  you 
may  begin  at  such  a  course  in  the  field  book  as  will  admit 
of  a  continual  addition  and  substraction ;  and  when  you  get 
to  the  bottom,  go  to  the  top,  and  you  will  end  in  cipher  at 
the  course  next  above  that  where  you  began. 


EXAMPLE     II. 


No. 

1. 
2. 
3. 
4. 
5. 
6. 
7. 

a 

9. 
10. 
IL 
12. 
13. 

Courses. 

Diet, 
rods. 

N. 

S. 

E. 

W. 

112 
11.7 

77.9 
62.1 

1  Dep. 
Col. 

46.0 
67.4 
114.1 
102.9 
91.2 
144.1 
158.5 
223.3 
145.4 
83.3 
83.3 
37.2 
00.0 

2  Dep. 
Col. 

North 
areas. 

South 
areas. 

N.  36°  45'  E. 
N.  22  30  E. 
&  7645  E. 
S.  15  00  W. 
S.  16  45  W. 
N.  75  00  E. 
N.  20  30  E. 
East 
S.  33  30  W. 
8.  76  00  W. 
North 
S.  84  00  W. 
N.  53  15  W. 

76.8 
56.0 
48.0 
43.4 
40.5 
54* 
41.2 
64.8 
141.2 
64.0 
36.0 
46.4 
46.4 

61.5 
51.7 

4.2 
38.6 

36.0 
27.8 

ii.o 

41.9 
38.8 

117.7 
15.5 

46.0 
21.4 
46.7 

529 
14.4 

64.8 

46.0 
113.4 
181.5 
217.0 
194.1 
235.3 
302.6 
381.8 
368.7 
228.7 
166.6 
120.5 
37.2 

2829.00 
5862.78 

3341.26 
11680.36 

1996.50 
9092.30 
7531.08 

5997.60 
1034.16 

43395.99 
3544.85 

590.45 

4.9 

46.1 
37.2 

110  Acres,  2  Roods,  and  23  Rods. 


DEMONSTRATION. 


Fig.  63. 


The  area  standing  against  the  1st  course,  is  the  triangle 
12t,  lying  without  the  field. 


72 

That  against  the  2d  course  is  the  trapezoid  23<w,  lying1 
without  the  field. 

That  against  the  3d  course  is  the  trapezoid  34#c,  and 
it  is  a  south  area,  lying  partly  within  and  partly  without  the 
field. 

That  against  the  4th  course  is  the  trapezoid  45cw,  and  it  is 
also  a  south  area. 

That  against  ?he  5th  course  is  the  trapezoid  56mo,  and  it  is 
also  a  south  area. 

That  against  the  6th  course  is  the  trapezoid  Q7no,  and  it 
is  a  north  area,  a  part  of  which  is  already  contained  in  two 
different  products.  In  this  area,  and  in  the  two  succeeding 
areas,  all  of  that  part  of  the  figure  which  lies  above  the 
line  06,  is  considered  void,  and  it  may  again  be  covered  by 
both  north  and  south  products. 

The  area  against  the  7th  course  is  the  trapezoid  78  en,  and 
it  is  a  north  area.  • 

Against  the  8th  course  there  is  no  latitude. 

The  area  against  the  9th  course  is  the  trapezoid  9,10,ea;  and 
it  is  a  south  area. 

That  against  the  10th  course  i&  the  trapezoid  10,  11,  xz,  and 
it  is  a  south  area. 

That  against  the  llth  station  is  the  parallelogram  11, 12,sz, 
and  is  a  north  area. 

That  against  the  12th  station  is  the  trapezoid  12,  13,s#,  and 
it  is  a  south  area. 

That  against  the  13th  station  is  the  triangle  13,1/y,  and  it 
is  a  north  area. 

When  the  field  is  very  irregularly  shaped,  it  will  often 
happen  that  parts  of  the  same  area  will  be  contained  in  sev- 
eral different  products  in  the  column  of  areas.  As  often  as 
a  space  is  cohered:  fey  a  north  product,  so  often  will  it  be 
covered  by  a  south  product ;  but  in  the  final  result,  the  sum 
of  one  column  being  substracted  from  that  of  the  other,  will 
leave  what  is  included  within  the  boundary  lines  of  the 
field. 

This  method  of  calculating  the  area  of  a  field  by  the  north- 
ings, southings,  eastings,  and  westings,  divides  the  field,  with 
a  certain  quantity  of  the  adjoining  ground,  into  right  angled 
triangles,  right  angled  trapezoids,  parallelograms,  or  squares, 
as  may  be  seen  by  the  figures.  It  may  therefore  with  pro- 
priety be  called  RECTANGULAR  SURVEYING.* 

*See  Appendis,  No.  6. 


, 

* 
SURVEYING.  73 


A  USEFUL  PROBLEM. 

To  FIND  THE  TRUE    AREA  OF  A  FIELD  WHICH  HAS   BEEN 
MEASURED  BY  A  CHAIN  TOO  LONG  OR  TOO  SHORT. 

Calculate  the  area  as  if  the  chain  was  of  a  true  length, 
then  institute  the  following  proportion. 

As  the  square  of  the  length  of  the  true  chain ; 
Is  to  the  area,  as  found  by  the  chain  made  use  of; 
So  is  the  square  of  the  length  of  that  chain; 
To  the  true  area  of  the  field. 


EXAMPLE. 

Suppose  a  field,  measured  by  a  two  rod  chain  3  inches  too 
long,  is  found  to  contain  41  acres  1  rood  and  33  rods,  what 
is  the  true  area. 

As  the  square  of  33  feet,  the  true  length  of  a  two  rod  chain ; 
is  to  41  acres  1  rood  and  33  rods;  so  is  the  square  of  33  feet 
3  inches,  the  length  of  the  chain  used  in  the  survey ;  to  42 
acres  and  13  rods.  33  feet=396  inches.  396X396=156816 
square  inches. 

41  acres  1  rood  33  rods=6633  rods. 

33  feet  3  inches=399  inches.  399X399=159201  square 
inches. 

159201X6633+156316=6733  rods. 

6733+160=42  acres  13  rods,  the  true  area. 


PART    II. 

LAYING  OUT  LAND. 

PROBLEM  I.  To  lay  out  any  number  of  acres  in  the 
form  of  a  square. 

Annex  5  ciphers  to  the  number  of  acres,  which  will  turn 
them  into  square  links,  the  square  root  of  which  will  be  the 
side  of  the  square  in  links. 

EXAMPLE  I.  It  is  required  to  lay  out  810  acres  in  the 
form  of  a  square. 

Answer.  Each  side  of  the  square  must  be  9000  links,  or 
90  chains. 

7» 


74 


SURVEYING. 


PROBLEM  II.     To  LAY  OUT  ANY  NUMBER  OF  ACRES  IPC 

THE    FORM    OF    A    PARALLELOGRAM,  WHEREOF    ONE    SIDE  IS 
GIVEN. 

Divide  the  number  of  acres  when  turned  into  square  links, 
by  the  given  side;  the  quotient  will  be  the  side  required. 

EXAMPLE.  What  must  be  the  longest  side  of  a  rectan- 
gle, which  is  to  contain  25  acres,  when  the  shortest  side  is  5 
chains  and  50  links  ?  ' 

Answer.  2500000-5-550=4545  links  for  the  longest  side. 

PROBLEM  III.     To  LAY  OUT  ANY  NUMBER  OF  ACRES 

IN  A  FIELD,  3,  4,  5,  6,  &C.  TIMES  AS  LONG  AS  IT  IS  BROAD. 

Divide  the  acres  when  turned  into  square  links,  by  the  ra- 
tio between  the  length  and  breadth  ;  the  square  root  of  the 
quotient  will  be  the  shortest  side. 

EXAMPLE.  It  is  required  to  lay  out  100  acres  5  times  as 
long  as  it  is  broad. 

Answer.  1 0000000-^-5=2000000,  .the  square  root  of  which 
is  1414  links  for  the  shortest  side,  and  the  longest  will  be 
7070  links. 

PROBLEM   IV.     To  MAKE  A  TRIANGLE  WHICH  SHALL 

CONTAIN    A    GIVEN  NUMBER  OF  ACRES,  BEING  CONFINED  TO 
A  CERTAIN  BASE. 

Double  the  given  number  of  acres,  to  which,  annex  5  ci- 
phers, and  divide  by  the  base  ;  the  quotient  will  be  the  per- 
pendicular height  in  links. 

EXAMPLE.  Upon  a  base  of  40  chains,  to  lay  out  100  acres 
in  a  triangular  form. 

Answer,  5000  links,  or  50  chains,  will  be  the  length  of  the 
perpendicular. 


The  perpendicular  may  be  erected 
from  any  part  of  the  base :  thus,  the 
triangle  ABC,  see  Fig.  64,  is  the  same 
as  AB  E,  each  containing  100  acres. 


SURVEYING. 


75 


When  the  given  base  is  so  situ- 
ated that  a  perpendicular  of  suffi- 
cient length  cannot  be  erected 
therefrom,  continue  the  base  as 
from  B  to  D,  Fig.  65,  from  which 
erect  the  perpendicular  D  C,  and 
complete  the  triangle  ABC, 
which  will  contain  100  acres. 


Fig.  65. 


PART    III. 

DIVIDING    LAND. 

As  different  fields  are  so  variously,  and  many  of  them  ir- 
regularly shaped,  and  as  they  are  required  to  be  divided  in 
many  different  proportions,  it  is  difficult  to  give  rules  which 
will  apply  to  particular  cases.  The  business  of  dividing  land 
must  therefore  be  left,  in  a  great  measure,  to  the  skill  and 
judgment  of  the  surveyor;  who,  if  he  is  well  acquainted  with 
trigonometry,  and  with  measuring  land,  will  not  find  it  diffi- 
cult, after  a  little  practice,  to  divide  a  field  in  such  a  manner 
as  shall  be  desired.  If  he  has  before  him  a  plot  of  the  field, 
and  knows  the  number  of  parts  into  which  it  is  to  be  divided, 
and  the  proportion  which  each  part  is  to  bear  to  the  others, 
he  will  readily  find  out  where  the  dividing  lines  are  to  be 
drawn. 

A  few  RULES  and  EXAMPLES  will  be  given  for  the  general 
instruction  of  the  learner. 


PROBLEM  I.    To  CUT  OFF  ANY  NUMBER  OF  ACRES  FROM 

A  SQUARE  OR   RECTANGLE. 

Say,  as  the  whole  number  of  acres  in  the  field  ;  is  to  the 
length  of  the  square  or  length  or  breadth  of  the  rectangle; 
so  is  the  number  of  acres  proposed  to  be  cut  off;  to  their 
proportion  of  the  length  or  breadth. 

*  *  '  '  . 
PROBLEM  II.    To  CUT  OFF  ANY  NUMBER  OF  ACRES  BY 

A  LINE  FROM  ANY  ANGLE  OF  A  TRIANGLE. 

Measure  the  base,  or  side  opposite  the  angle  from  which 


76 


SURVEYING. 


the  dividing  line  is  to  be  drawn;  then  say,  as  the  number  of 
acres  in  the  whole  triangle  ;  is  to  the  whole  base  ;  so  is  the 
given  number  of  acres;  to  their  part  of  the  base. 

Fig.,  66. 


EXAMPLE.     See  Fig.  66. 


In  the  triangle  ABC,  which  contains  48  acres,  it  is  required 
to  cut  off  18  acres,  by  a  line  proceeding  from  C  to  the  base 
A  B,  which  is  40  chains. 

As  48:  40:  :  18  :  15 

Lay  15  chains  on  the  base  from  B  to  D,  and  draw  the  line 
C  D.  The  triangle  will  then  be  divided  as  was  proposed ; 
BCD,  containing  18  acres. 

PROBLEM  III.     To  TAKE  OFF  ANY  GIVEN  NUMBER  OF 

ACRES  FROM  A  MULTANGULAR  FIELD. 


EXAMPLE  I.  See  Fig.  67.  B 


Let  A  B  C  D,  &c.  be  the  plot  of  a  field  containing  1 1  acres, 
from  which  it  is  required  to  cut  off  5  acres. 

Join  two  opposite  corners  of  the  field,  as  D  and  G,  with  the 
line  D  G,  (which  you  may  judge  to  be  near  the  partition  line,) 
and  find  the  area  of  the  part  D  E  F  G,  which,  suppose,  may 
want  140  rods  of  the  quantity  proposed  to  be  cut  off  Mea- 
sure the  line  D  G,  which,  suppose  to  be  70  rods;  divide  140 
by  35,  the  half  of  D  G,  and  the  quotient  4  will  be  the  length  of 
the  perpendicular  of  a  triangle,  whose,  base  is  70  and  the  area 
140.  Lay  off  4  rods  from  G  to  I,  and  draw  the  line  D  I, 
which  will  be  the  dividing  line.* 

*This  explanation  supposes  DGand  AG  alright  angles  to  each 
ether.  When  they  are  not  at  right  angles,  the  height  G  I  most  not 
be  measured  on  the  side  of  the  field. — ED.  • 


SURVEYING, 

EXAMPLE  II.     See  Fig.  68. 


Let  ABC  D,  /&c.  be  a  tract  of 
land  to  be  divided  into  two  equal 
•parts,  by  a  line  from  I  to  the  oppo- 
site  side  C  D ;  to  find  arithmetically 
on  what  part  of  the  line  C  D  the  di- 
viding line  I  N  will  fall ;  or  to  find 
the  distance  C  N. 


Fig.  68. 


FIELD  BOOK. 

Rods. 

AB. 

N. 

19° 

0' 

E. 

108 

FG. 

W 

BC. 

S. 

77 

0 

E. 

91 

GH. 

N. 

CD. 

S. 

27 

0 

E. 

115 

HI. 

Nc 

DE. 

S. 

52 

0 

W. 

58 

I  A. 

N. 

EF. 

S. 

15 

30 

E. 

76 

Rods. 

t  70.9 

36°    0'    W.  47 
h  64.3 

62     15      W.  59 

Acres  Rood  Rods. 
Whole  area  152—  1  —"25 

Find  the  area  of  the  part  I  A  B  C,  according  to  SECTION 
III.  page  64,  as  follows  :  set  the  latitude  and  departure  of  the 
three  first  sides,  I  A,  A  B,  and  B  C,  in  their  proper  columns, 
in  a  traverse  table  5  and  place  as  much  southing,  viz.  109.1, 
equal  to  the  line  C  K,  and  as  much  westing,  viz.  71.7, 
equal  to  the  line  K  I,  as  will  balance  the  columns.  This 
southing  and  westing  will  be  the  latitude  and  departure  made 
by  the  line  C  I.  The  area  of  I  A  B  C  will  be  found  to  be 
8722  rods,  which  is  less  than  half  the  area  of  the  whole  field 
by  3470  rods,  the  quantity  to  be  contained  in  the  triangle  I  C  N. 
Find  the  bearing  and  distance  of  C  I  by  RIGHT  ANGLED 
TRIGONOMETRY,  CASE'  IV.  as  follows:* 

As  C  K,  the  southing  of  C  I,  109,  nearly        -       2.037426 

:  radius    - 10000000 

: :  K.I,  the  westing  of  C  I,  71.7        -        -       -        1.855519 


:  tangent  course  S.  33°  20'  W. 


11855519 
2  037426 

9.818093 


*  The  mode  given  above  is  undoubtedly  the  most  correct,  but  the  use 
of  the  traverse  table  will  save  many  figures.  From  that  table  the 
course  and  distance  of  C  I,  may  be  found  at  sight. — ED. 


78  SURVEYING. 

As  sine  course  33°  20'            ....  9.739975 

:  departure  K  I,  71.7 1.855519 

::  radius 10.000000 


11.855519 

9.739975 

:  Distance  I C  130.5        -        -        -        •        -        2.115544 


NOTE.    In  this  way  the  course  and  distance  may  be  found  from,  any 
angle  of  a  field  to  another. 

Having  found  the  line  C  I,  divide  3470,  the  number  of  rods 
to  be  contained  in  the  triangle  I  C  N,  by  one  half  the  line  C  I, 
viz.  65.25  ;  the  quotient  will  be  the  length  of  the  perpendicu- 
lar PN,  viz.  53.18. 

Now,  by  the  bearings  of  C  I  and  C  D,  it  appears  that  they 
form  an  angle  of  60°  20' ;  wherefore,  in  the  triangle  C  P  N, 
are  given  the  side  P  N  53.18,  and  the  angle  at  C  60°  20',  to 
find  the  hypothenuse  C  N. 

As  sine  P  C  N  60°  20'  -         -         9.938980 

:sidePN53.18  -         -         -         1.725748 

:  :  radius  ....       10.000000 


11.725748 
9.938980 

:  hyp.  ON  61.2  -  1.78676& 

Thus  the  dividing  line  must  go  from  I  to  a  point  on  the 
line  C  D,  which  is  61.2  rods  from  C.  The  bearing  and  dis- 
tance of  this  line  may  be  found  by  the  directions  given  above 
for  finding  the  bearing  and  distance  of  the  line  C  I.  Or,  they 
may  be  found  by  oblique  trigonometry,  CASE  III. 

ANOTHER  METHOD  OF  FINDING   THE  DISTANCE  C  N. 

Having  ascertained  the  latitude  and  departure  of  the  line 
C  I,  set  them  down  in  a  traverse  table ;  find  the  latitude  and 
departure  of  the  line  C  D,  and  place  them  in  the  table;  the 
difference  between  the  northing  of  the  line  I  C,  and  the 
southing  of  the  line  C  D,  will  be  the  southing  of  the  line  D  I, 
viz.  6.6 ;  and  the  sum  of  the  eastings  of  those  lines,  as  they 
are  both  easterly,  will  be  the  westing  of  the  line  DI,  viz. 
123.9.  Proceed  to  calculate  the  area  of  the  triangle  I  C  Df 
which  will  be  found  to  be  6522  rods,  nearly. 

NOTE.    As  in  this  triangle  two  sides  and  their  contained  angle  are 
given,  the  area  may  be  found  by  PROB.  IX.  Rule  4.  page  42. 


SURVEYING.  79 

Having  found  the  area  of  this  triangle,  proceed  to  find 
C  N  according  to  PR  OB.  II.  page  75,  as  follows  : 

As  the  area  of  the  triangle  ;  is  to  C  D  the  base ;  so  is  the 
quantity  to  be  contained  in  the  triangle  I  C  N  ;  to  C  N,  its  pro- 
portion of  the  base. 

As  6522:  115:  :  3470  :  61.19. 


A  THIRD   METHOD  OF  FINDING  THE  DISTANCE  C  N. 

To  the  logarithm  of  double  the  area  to  be  contained  with- 
in the  triangle  I  C  N,  add  radius  ;  from  this  sum  substract  the 
logarithmic  sine  of  the  angle  at  C ;  and  from  the  remain- 
der substract  the  logarithm  of  the  side  1C  ;  the  last  remainder 
will  be  the  logarithm  of  the  side  C  N. 

The  double  area  of  the  triangle  I  C  N,  is  6940 ;  the  angle 
at  C  is  60°  20' ;  the  side  I  C  is  130. 

Double  area  6940  -         -         3.841359 

Radius  -        -         -       10.000000 


13.841359 
Sine  I C  N  60°  20'  -         9.938980 


3.902379 
Side  1C  130.5  -         -         -         2.115544* 


Side  CN  61.21  -         -         1.786835 


NOTE.  Radius  may  be  added  by  placing  a  unit  before  the  index  of 
the  logarithm  for  the  double  area,  without  the  trouble  of  setting 
down  the  ciphers. 


BY  NATURAL  SINES. 

Divide  the  double  area  by  the  natural  sine  of  the  given 
angle,  and  that  quotient  by  the  given  side ;  the  last  quotient 
will  be  the  side  C  N. 

Nat.  sine  of  the  angle  at  6  60°  20'  0.86892 

6940-0.86892=7986.92 

7986.92-^-130.5=61.2 

*  The  log.  of  I  C,  as  found  by  calculation  on  page  77,  is  employed, 
instead  of  taking  from  the  tables,  that  of  130.5,  which  is  not  the  exact 
length  of  I  C.— ED. 


80  SURVEYING. 

From  the  above  the  following  general  rule  may  be  drawn. 

To  FIND- THE. SIDE  OF  A  TRIANGLE  WHEN  THE  AREA  IS 
GIVEN,  AND  ALSO  ONE  OF  THE  SIDES,  AND  THE  ANGLE  CON- 
TAINED BETWEEN  THE  GIVEN  SIDE  AND  THE  SIDE  REQUIRED. 

To  THE  LOGARITHM  OF  DOUBLE  THE  AREA  ADD  RADIUS  J 
FROM  THIS  SUM  SUBSTRACT  THE  LOGARITHMIC  SINE  OF  THE 
GIVEN  ANGLE,  AND  FROM  THE  REMAINDER  SUBSTRACT  THE 
LOGARITHM  OF  THE  GIVEN  SIDE  J  THE  LAST  REMAINDER 
WILL  BE  THE  LOGARITHM  OF  THE  SIDE  REQUIRED. 

OR,  BY  NATURAL  SINES  I  DIVIDE  THE  DOUBLE  AREA 
BY  THE  NAT.  SINE  OF  THE  GIVEN  ANGLE,  AND  THAT  QUOTI- 
ENT BY  THE  GIVEN  SIDE  J  THE  LAST  QUOTIENT  WILL  BE 
THE  SIDE  REQUIRED. 


CONCLUDING  REMARKS. 

Other  methods  of  surveying-  fields  are  taught  by  some 
authors  on  this  subject.  The  preceding,  however,  will  be 
found  most  useful  in  actual  practice.  Other  instruments  be- 
sides those  mentioned  in  this  book  ar.e  sometimes  used;  such 
as  the  plain  table,  semicircle,  perambulator,  theodolite,  &c. 
But  of  these  instruments  very  little  use  is  made  in  New 
England ;  and  they  are  not  often  to  -be  met  with.  For  gene- 
ral practice,  none  will  be  found  more  useful  than  a  common 
chain,  and  a  compass  upon  Rittenhouse's  construction. 

It  will  be  observed  that  in  this  work  there  is  no  descrip- 
tions of  mathematical  and  surveying  instruments.  The  com- 
piler omitted  such  descriptions,  from  a  belief  that  nothing 
which  can  be  written  on  the  subject  will  enable  a  person  to 
understand  them,  without  an  actual  inspection  of  the  instru- 
ments themselves,  and  some  instruction  from  those  acquainted 
with  them. 

;     The  general  principles  here  taught  may  be  applied  to  the 
surveying  of  townships,  roads,  rivers,  harbours,  &c. 


APPENDIX. 


OF  THE  DECLINATION  AND  VARIATION  OF  THE  MAGNETIC 
NEEDLE,  AND  OF  THE  ATTRACTIONS  TO  WHICH  IT  IS 
SUBJECT. 

THE  declination  of  the  needle  is  the  number  of  degrees  it 
deviates  from  the  true  north,  either  east  or  west.  This  dif- 
fers in  different  places,  and  in  the  same  place  at  different 
times.  [At  Hartford,  Conn.,  the  declination  was,  in  1829,  6° 
3'  west  of  the  true  meridian  of  the  earth ;  and  was  increasing 
by  an  annual  variation  of  about  3'.] 

The  following  method  of  ascertaining  the  variation,  by  the 
north  star,  has  been  adopted  by  many  surveyors,  as  the  most 
eligible  to  be  practised  on  land.  It  was  communicated  to 
the  compiler  by  Moses  Warren,  Esq.,  of  Lyme,  an  experi- 
enced surveyor,  with  permission  to  publish  it. 

The  star,  commonly  called  the  north  star,  is  not  directly 
north,  but  revolves  round  the  pole  in  a  small  circle,  once  in 
24  hours.*  It  can  therefore  be  due  north  only  twice  in  that 
period ;  and  that  is  within  a  very  few  minutes  of  the  time, 
when  a  star,  called  Alioth,  in  the  constellation  of  Ursa  ma- 
jor, or  the  great  bear,  is  directly  over  or  under  it.  There  is 
also  another  star  nearly  in  an  opposite  direction  from  the 
pole,  called  Gamma,  in  the  constellation  of  Cassiopeia. 
When  these  three  stars  are  vertical,  the  north  star  is  very 
near  the  meridian  ;  and  when  they  are  horizontal,  it  is  at  its 
greatest  elongation,  that  is,  at  its  greatest  distance  east  or 
west  of  the  pole,  and  on  the  same  side  as  the  star  in  Cassio- 
peia. The  variation  may  be  calculated  when  the  star  is  on 
the  meridian,  or  when  at  its  greatest  elongation ;  more  accu- 
rately, however,  at  the  latter  period,  because  its  motion  be- 

*  More  exactly,  23  hours,  56  minutes,  and  4  seconds. — Enr 
8 


0*A  APPENDIX. 

ing  then  nearly  vertical  for  some  time,  gives  the  observer 
opportunity  to  complete 'his  observation.* 

To  find  the  elongation  of  this  star  in  any  latitude,  its  de- 
clination must  be  known :  that  is,  its  distance  north  of  the 
equator.  This  being  found,  institute  the  following  pro- 
portion : 

As  co-sine  of  the  latitude;  is  to  radius ;  so  is  co-sine  of  the 
declination;  to  sine  of  the  elongation. f 

The  declination  of  the  north  star,  January  1,  1810,  was 
88°  17'  28",  and  increasing  at  the  rate  of  about  19  seconds 
and  one  half  annually. 

In  the  following  table,  the  elongation  is  calculated  for  ten 
successive  years,  ending  with  1840,  and  for  seven  different 
latitudes.  The  calculation  is  made  for  the  first  of  July,  and 
of  course  gives  the  mean  angle  for  the  year. 


TABLE  SHOWING  THE  ELONGATION  OF  THE  NORTH  STAR. 


Years 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

1831 

l°52i' 

1°55' 

l°58i' 

2°  If 

2°  5' 

2°  9' 

2°  13' 

1832 

52 

1  54i 

58  * 

2   \2 

2   41' 

2   81 

2  12f 

1833 

51i 

1  54* 

57i 

9   01 
6    U.2 

2   4* 

2   8" 

2  12f 

1834 

51 

1  53i 

57 

2   4 

2   7-i 

u 

2  12* 

1835 

50i 

1  53 

56i 

1   59" 

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*  The  following  figure  exhibits  a  view  of  tne  relative  situation  of 
these  stars,  as  they  appear,  when  in  a  horizontal  position;  or  when  the 
north  star  is  in  its  greatest  eastern  elongation. 


The  Great  Bear. 


Cassiopeia. 


Alioth 


N.  Star. 

* 


Gamma  * 


t  This  angle  is  usually  called  azimuth, — ED. 


APPENDIX.  83 

The  elongation  for  the  latitude  of  the  observation  being 
calculated  or  taken  from  the  above  table,  proceed  to  find  its 
range  according  to  the  following  directions  : 

Take  a  pole,  18  or  20  feet  in  length ;  to  the  end  of  it  fasten 
a  small  line;  raise  it  to  an  elevation  of  45°  or  50°  ;  and  sup» 
port  it  by  two  crotches  of  suitable  height,  to  keep  it  firm  in 
its  place.  At  the  end  of  the  line,  near  the  ground,  fasten  a 
weight  of  half  a  pound  or  more,  which  should  swim  in  water 
to  prevent  the  air  from  moving  the  line.  Southward  of  the 
line  fix  a  compass  sight,  or  other  piece  of  metal  or  wood,  with 
a  narrow,  perpendicular  aperture,  at  a  convenient  height  from 
the  ground,  say  about  2  or  21  feet ;  and'let  it  be  so  fixed  that  it 
can  be  moved  a  small  distance  east  or  west  at  pleasure.  Let  an 
assistant  hold  a  light  either  N.  E.  or  N.  W.  of  the  line,  near- 
ly as  high  as  the  range  from  the  sight  to  the  north  star,  in 
such  a  position  that  the  line  may  plainly  be  seen ;  then,  (the 
three  stars  above  mentioned  being  parallel,  or  nearly  so,  with 
the  horizon,)  move  the  sight-vane  east  or  west,  until,  through 
the  aperture,  the  line  is  seen  to  cut  the  star ;  and  continue  to 
observe,  at  short  intervals,  till  the  star  is  seen  at  its  greatest 
elongation.  Let  a  lighted  candle  be  placed  in  an  exact  range 
with  the  sight-vane  and  line,  at  the  distance  of  20  rods  or 
more,  which  should  stand  perpendicularly,  be  made  fast, 
extinguished,  and  left  till  morning.  Then  the  sight-vane, 
the  line,  and  the  candle,  will  be  the  range  of  elongation, 
which  observe  accurately  with  a  compass ;  and  if  the  elon- 
gation be  east  and  the  variation  west,  the  former  must  be  sub- 
stracted  from  the  latter ;  and  if  they  are  both  west,  they  must 
be  added,  and  their  difference  or  sum  will  be  the  true 
variation.* 


OF  THE  ATTRACTION  OF  THE  NEEDLE. 

It  is  well  known  that  any  iron  substance  has  an  influence 
upon  the  magnetic  needle,  attracting  it  one  way  or  the  other 
upon  the  point  where  it  would  settle,  were  there  no  such  at- 
traction. A  surveyor  should  therefore  be  careful  to  see  that 
no  iron  is  near  the  compass  when  taking  a  bearing.  But  as 
the  earth,  in  certain  spots,  contains,  near  its  surface,  iron,  or 
other  minerals,  which  attract  the  needle,  it  will  frequently 

*  The  author,  in  common  with  many  writers,  employs  the  term  va- 
riation,  as  synonymous  with  declination.  Variation  is  properly,  how* 
ever,  the  change  of  declination. — ED. 


84  APPENDIX. 

happen  that  it  will  point  wrong.  To  ascertain  whether  this 
is  the  case,  the  surveyor,  at  each  station,  should  take  a  back 
view  of  the  one  last  left ;  and  if  he  finds  that  the  compass 
does  not  reverse  truly,  he  may  be  sure,  provided  the  compass 
be  accurately  graduated  and  placed  horizontally,  that  he  either 
made  a  mistake  at  the  last  station,  or  that  in  one  or  the  other, 
or  both  of  the  stations,  the  needle  was  attracted  from  the 
true  point.  When  he  finds  a  place  where  he  suspects  there 
is  an  attraction,  he  should  go  a  few  rods  backward  or  forward, 
and  see  whether  the  needle  points  differently.  In  this  way 
he  may  prevent  mistakes  in  his  field  notes,  which  would  arise 
from  putting  down  a  wrong  course.  To  take  back  sights  is 
particularly  necessary  in  running  long  lines,  and  laying  out 
new  lands,  where  the  needle  is  the  only  thing  to  guide  the 
surveyor. 

By  practice  and  experience,  a  knowledge  will  be  acquired 
on  this  subject,  and  with  regard  to  many  other  things  in  sur- 
veying, which  cannot  be  taught  by  books ;  and  after  all  the 
directions  which  can  be  written,  the  practitioner  will  frequent- 
ly find  occasion  for  the  exercise  of  his  own  judgment. 


A  RULE  TO  FIND  THE  DIFFERENCE  BETWEEN  THE  PRE- 
SENT VARIATION  OF  THE  COMPASS,  AND  THAT  AT  A  TIME 
WHEN  A  TRACT  WAS  FORMERLY  SURVEYED,  IN  ORDER  TO 
TRACE  OR  RUN  OUT  THE  ORIGINAL  LINES. 

Go  to  any  part  of  the  premises,  where  any  two  adjacent 
corners  are  known ;  and  if  one  can  be  seen  from  the  other, 
take  their  bearing ;  which,  compared  with  that  of  the  same 
line  in  the  former  survey,  shows  the  difference.  But  if  one 
corner  cannot  be  seen  from  the  other,  run  the  line  according 
to  the  given  bearing,  and  observe  the  nearest  distance  be- 
tween the  line  so  run,  and  the  corner ;  and  then  work  the 
following  proportion : 

As  THE  LENGTH  OF  THE  WHOLE  LINE, 

Is  TO  57.3  DEGREES,* 

So  IS  THE  SAID  DISTANCE, 

To  THE  DIFFERENCE  OF  VARIATION  REQUIRED. 

EXAMPLE. 

Suppose  it  be  required  to  run  a  line,  which,  some  years 
ago,  bore  N.  45°  E.,  distance  20  chains,  and  in  running  this 

*  57.3  degrees  is  the  radius  of  a  circle  (nearly)  in  such  parts  that  the 
circumference  contains  360. 


APPENDIX.  85 

line  by  the  given  bearing-,  the  corner  is  found  20  links  to  the 
left  hand;  what  is  the  present  bearing  of  this  line? 

Ch.  Deg.  L. 

As  20     :     57.3  :  :  20 
100          20 


2000  1146.0 
60 

2000)68760(34  Minutes. 

Answer —  34  minutes  to  the  left  hand  is  the  allowance  re- 
quired, and  the  line  in  question  bears  N.  44°  26'  E. 


The  compiler  of  this  work  acknowledges  himself  under 
obligations  to  George  Gillet,  Esq.,  Surveyor  General  of  the 
state  of  Connecticut,  for  the  following  illustrations,  remarks, 
and  miscellaneous  questions,  considering  them  calculated  to 
be  useful  to  the  learner,  and  the  practical  surveyor. 


PRACTICAL  TRIGONOMETRY. 


The  learner  must  understand  decimals,  and  the  nature  and 
use  of  logarithms,  before  he  can  make  any  proficiency  in 
this  branch.  Difference  of  latitude  is  the  distance  between 
the  parallels  of  the  beginning  and  of  the  terminating  point 
of  a  line,  or  of  any  number  of  lines,  whether  northerly  or 
southerly.  Departure  is  the  distance  between  the  meridians 
of  the  beginning  and  of  the  terminating  point,  or  the  dis- 
tance made  either  east  or  west  from  any  particular  meridian 
on  any  course. 

These  distances  are  also  called  northings  or  southings, 
eastings  or  westings,  as  different  cases  may  happen. 

When  a  course  and  distance  are  given,  the  distance  is  the 
hypothenuse  of  a  right  angled  triangle,  of  which  the  latitude 
and  departure  are  the  legs.  The  angle  which  the  course 
makes  with  the  meridian,  is  opposite  to  the  departure.  Sub- 
stract  the  course  from  90°,  and  the  remainder  will  be  the 
quantity  of  the  angle  opposite  to  the  latitude. 

8* 


APPENDIX. 


CASE 

In    the    annexed    triangle,   the 
side  A  C,  is  given  N.  40°  W.  50 
rods.     The  latitude  and  departure, 
or  the  northing  and  westing,  a 
required. 

A  B  is  a  meridian,  or  a  north 
and  south  line.  The  angle  at  A 
contains  40°,  and  that  at  C,  50°,  as 
appears  by  their  respective  arches. 
B  C,  is  an  east  and  west  line,  of 
course  the  angle  at  B  contains  90°, 
or  it  is  a  right  angle.  A  C  is  made  radius.  From  the  point 
at  A,  the  arch  C  a  is  described.  From  the  point  at  C,  the 
arch  A  z  is  described.  B  C  is  the  sine  of  the  angle  at  A,  or 
of  the  arch  C  a,  and  A  B  is  the  co-sine.  A  B  is  the  sine  of 
the  angle  at  C,  or  of  the  arch  A  z,  and  B  C  is  the  co-sine. 
Sines  and  co-sines  lie  within  their  respective  arches.  Each 
side  is  proportioned  to  its  opposite  angle,  and  each  angle  to  its 
opposite  side. 


TO  FIND  THE  REQUIRED  SIDES,  TAKE  THE  FOLLOWING  RULE. 

For  the  latitude,  make  radius,  the  angle  at  B,  the  first 
term, — the  logarithm  of  the  side  A  C  50,  the  second ;  the 
sine  of  the  angle  at  C,  the  third,  and  the  fourth  will  be  the 
logarithm  of  the  latitude  A  B.  For  the  departure,  take  the 
same  first  and  second  terms,  the  sine  of  the  angle  at  A  for 
the  third%  and  the  fourth  will  be  the  logarithm  of  the  de- 
parture B  C. 

SEE  THEM  WORKED  : 


As  radius,  -  10.000000 
:  side  AC,  50  rods,  1.698970 
:.;sineofC,  50°,  9.884254 


Radius, 


11.583224 
10.000000 


•.Latitude  38.30  rods,  1.583224 


As  radius,  -  10.000000 
:  side  A  C,  50  rods,  1.698970 
:  :  sine  of  A  40°,  9.808067 


Radius, 


11.507037 
10.000000 


:departure,32.14rods,1.507037 


APPENDIX. 


87 


Required  the  latitude  and  departure  of  S.  28°,  W.  88  rods. 
As  radius  -        10.000000    As  radius,  -        10.000000 


:  distance  88,  logarithm,    1.944483 
: :  cosine  of  course  28°     9.945935 


11.890418 
10.000000 


:  latitude,  77.70, 


1.890418 


:  distance,  88  rods, 


1.944483 


:  :  sine  of  the  course  28°  9.671609 


:  departure,  41.31, 


11.61609-2 
10.000000 

1.616092 


Required  the  latitude  and  departure  of  N.  75°,  E.  245  rods. 


As  radius,  -  10.000000 

.  distance  245,      -  2.389166 

: :  co-sine  of  course,  75°    9.412996 


latitude,  63.41, 


11.802162 
10.000000 

1.802162 


As  radius, 

:  distance,  245, 

: :  sine  of  the  course 


:  departure,  236.65, 


10.000000 
2.389166 
9.984944 

12.374110 
10.000000 

2.374110 


The  logarithm  of  the  distance  may  be  set  down  in  two 
places ;  and  the  sine  of  the  course  may  be  placed  under 
one,  and  the  co-sine  under  the  other,  and  when  they  are 
added,  the  unit  at  the  left  hand,  in  each  case,  may  be  cancelled, 
which  will  be  the  same  as  subtracting  radius. 


CASE    II. 


Fig.  2. 


ISO 


Suppose  you  run  north  from  A  to  B,  220  * 
rods;  then  east  150  rods  to  C.  What  is 
your  course  and  distance  from  C  to  A? 
First  find  the  course.  In  this  case,  make 
the  side  A  B  radius.  With  your  dividers 
on  the  point  at  A,  describe  the  arch  Ba, 
then  on  the  point  at  C,  describe  the  arch 
B  z.  In  describing  the  last  arch  B  C  is 
made  radius.  Each  arch  contains  as  ma- 
ny degrees  as  its  opposite  angle. 

As  the  sides  AB  and  B  C,  both  lie  without  their  respective 
arches,  they  are  tangents.  B  C  is  the  tangent  of  the  angle  at 
A,  or  of  the  arch  B  a,  and  A  B  is  the  co-tangent.  A  B  is  the 
tangent  of  the  angle  at  C,  or  of  the  arch  B  z,  and  B  C  is 
the  co-tangent. 


88 


APPENDIX. 


NOTE.    When  an  angle  is  required,  a  side  must  be  the  first  term. 
When  a  side  is  required,  an  angle  must  be  the  first  term. 

To  find  the  course  from  C  to  A,  Fig.  2,  adopt  the  follow- 
ing  rule. 

Suppose  yourself  standing  at  the  angle  A ;  make  the  side 
A  B  radius,  then  state :  as  the  log.  of  the  side  A  B  220  ;  is  to 
radius  ;  so  is  the  log.  of  the  side  B  C,   150,  to  the  tangent  of 
the  angle  at  A.     See  the  example  worked. 
As  log.  of  A  B, 

220—2.342423  :  R.  10,000000  :  :  log.  B  C,  150—2.176091 
2.176091 


12.176091 
2.342423 

:  Tang,  of  A  34°  17'     9.833668 


In  the  column  of  tangents,  under  34°  against  17',  you  will 
find  the  last  term,  or  that  which  is  nearest  to  it.  The  course 
from  A  to  C  is  N.  34°  17'  E.,  or  from  C  to  A,  S.  34°  17'  W. 
Next  find  the  distance. 


CASE    III. 

TO  FIND  THE    DISTANCE. 

Make  the  side  A  C  radius.  From  the 
point  at  A  describe  the  arch  C  x.  In 
this  case,  the  side  B  C  is  a  sine,  as  it 
lies  within  the  arch.  Take  the  follow- 
ing rule. 

As  the  sine  of  the  angle  at  A,  is  to 
the  side  B  C,  so  is  radius  to  the  side 
A  C.  See  the  example  worked. 


As  sine  of  A  34°  17' 
:  side  B  C,  150, 
: :  radius, 


A 

9.750729 

2.176091 

10.000000 

12.176091 
9.750729 


side  A  C,  266.3 


2.425362 


APPENDIX. 


Suppose  you  begin  at  a  pine,  and  run  north  125  rods  to  a 
hemlock,  then  east  216£  rods  to  a  spruce,  what  is  the  course 
and  distance  from  the  spruce  to  the  pine  ?  By  CASE  II.  find 
the  course,  and  by  CASE  III.  the  distance.  Suppose  your- 
self standing  at  the  pine,  and  making  the  northing  radius, 
the  proportion  will  be, 

As  125,  2.096910 

:  radius,  10.000000 

::  216.5  2.335458 


12.335458 
2.096910- 

:  tang,  at  the  pine,  60°,  10.238548 


The  course  from  the  spruce  to  the  pine  is  S  60°  W. 

NOTE.    As  the  easting  is  greater  than  the  northing,  the  course  is  over 
45°,  therefore  look  at  the  bottom  of  the  page  to  find  it. 

To  find  the  distance  from  the  spruce  to  the  pine,  make 
that  side  radius?  and  the  proportion  will  be,  as  the  sine  of 
the  angle  at  the  pine  ;  is  to  the  easting;  so  is  radius  to  the 
distance  required :  or,  as  the  sine  of  the  angle  at  the  spruce  : 
is  to  the  northing ;  so  is  radius  to  the  distance  from  the  spruce 
to  the  pine. 


As  sine  at  the  pine  60°     9.937531 
:  the  easting  -216.5,  2.335458 

:  :  radius  10.000000 


12.335458 
9.937531 

required  dist.  250  rods,     2.397927 


As  sine  at  the  spruce  30°  9.698970 
:  northing,  125,  2.096910 

:  :  radius,  10.000000 

12.096910 
9.698970 

:  required  dist.  250  rods,    2.397940 


The  following  courses  and  distances  of  a  survey  are  giv- 
en, and  the  course  and  distance  of  the  closing  line  are  re- 
quired. 

Beginning  at  a  maple  tree,  thence  running  as  follows: — 
S.  80°  W.  90  rods,  N.  15°  W.  95  rods,  N.  85°  E.  45  rods, 
S.  10°  E.  40  rods,  N.  85°  E.  42  rods,  to  a  beech  tree.  First, 
arrange  the  given  courses  and  distances  in  a  table,  having  a 
blank  line  for  the  course,  distance,  latitude,  and  departure  of 
the  closing  line.  Find  by  the  traverse  table  the  latitude  and 
departure  of  each  course  and  distance,  and  insert  them  in 
their  respective  columns  as  follows : — 


90 


APPENDIX. 


No. 

Courses. 

Dist. 

N. 

S. 

E. 

W- 

I 

S.  80°  AV. 

90.0 

15.63 

88.63 

2 

N.  15°  W. 

95.0 

91.76 

24.59 

3 

4 

N.  85°  E. 

45.0 

3.92 

1  44.83 

S.  10°  E. 

40.0 

39.39   |     6.95 

5 

N.  85°  E. 

42.0 

3.66 

41.84 



44.32 

19.60 

99.34 

99.34   '113.22 

113.22 

Substract  the  sum  of  the  southings  from  that  of  the  north- 
ings, and  44.32  will  remain  to  fill  the  blank  in  the  column 
of  southings.  Also,  substract  the  sum  of  the  eastings  from, 
that  of  the  westings,  and  19.60  will  remain  to  fill  the  blank 
in  the  column  of  eastings. 

These  numbers  or  distances  are  the  legs  of  a  right  angled 
triangle,  the  hypothenuse  of  which  is  the  closing  line. 

You  are  now  standing  at  the  beech  tree.  Make  the 
southing  radius,  and  to  find  the  course,  the  proportion  will  be, 


As  the  southing  44.32, 

:  radius, 

:  :  the  easting  19.60, 


1.646600 

10.000000 

1.292256 

11.292256 
1.646600 


: :  tangent  of  the  course,  23°  51'    9.645656 


The  course  of  the  closing  line  is  S.  23°  51'  E.  which 
may  fill  the  blank  in  the  column  of  courses. 

To  find  the  distance,  make  the  line  from  the  beech  to  the 
maple,  or  the  closing  line,  radius,  and  the  easting  will  be  a 
sine,  then  state, 


APPENDIX.  91 


As  the  sine  of  the  course  23°  51'    9.606751 
:  the  easting,  19.60.  1.292256 

:  :  radius,  10.000000 


11.292256 

9.606751 

• 

:  the  distance,  48.48  rods,  1.685505 


The  distance  is  48.48  rods,  which  may  be  entered  in  the 
blank  space  in  the  column  of  distances,  and  the  survey  will 
be  complete. 

In  the  table  of  logarithms,  against  484,  in  the  column  un- 
der 8,  the  last  term,  or  the  logarithm  which  is  nearest  to  it,  is 
found  :  8  must  be  annexed  to  484,  and  as  the  index  is  a  unit, 
or  1,  the  two  left  hand  figures  are  integers,  and  the  others  are 
decimals. 

Former  editions  of  this  work  contained  several  cases  in 
Rectangular  Trigonometry,  which  depended  on  secants  for 
solution,  but  as  secants  are  not  retained  in  the  tables  which 
accompany  this  edition,  those  cases  are  also  excluded  from 
it.  In  Practical  Surveying,  no  case  will  occur,  which  cannot 
be  solved  by  these  tables,  nor  can  one  occur,  which  depends 
on  a  solution  by  Rectangular  Trigonometry,  and  which  can- 
not be  solved  by  the  cases  here  treated  of;  therefore,  secants 
are  of  no  use  to  the  practical  surveyor. 

Young  learners  meet  with  much  perplexity  in  giving  de- 
cimals their  proper  places  when  calculating  latitudes  and  de- 
partures by  inspection  from  the  traverse  table.  This  sub- 
ject claims  some  attention. 

What  is  the  latitude  and  departure  of  N.  84°  E.  70  rods 
and  2  links  ? 

The  distance  is  70.08  rods.  The  decimal  is  8.100  of  a 
rod.  Over  84°  in  the  traverse  table  against  70,  the  lat.  is 
7.32,  and  the  dep.  is  69.62. 

Against  8r  over  latitude  is  0.84,  so  nigh  a  unit  that  one 
may  be  added  to  the  second  decimal  in  the  lat.,  and  over  dep. 
is  7.98,  so  near  8  that  that  number  may  be  added  to  the  see- 
ond  decimal  in  the  departure.  Ans.  lat.  7.33,  dep.  69.70. 

When  a  course  departs  10°  from  a  meridian,  and  it  is  re- 
quired to  add  the  lat.  and  dep.  of  10  links  or  .40  of  a  rod  to 
the  lat.  and  dep.  of  the  number  of  rods  contained  in  the  dis- 
tance; under  10°  against  40,  the  lat.  is  39.39,  and  the  dep.  is 
6.95.  As  the  two  right  hand  figures  of  the  latitude  are  un- 
der 50,  they  may  be  rejected,  and  as  the  two  right  hand  fig- 


92  APPENDIX. 

ures  of  the  dep.  are  over  50,  a  unit,  or  1,  may  be  added  to  the 
left  hand  figure  and  the  two  last  rejected,  and  the  answer 
will  stand,  lat.  .39,  dep.  .07.  If  the  decimal  is  called  4  tenths, 
the  separating  point  in  both  lat.  and  dep.  may  be  carried  over 
one  figure,  towards  the  right,  adding  a  unit  to  the  dep.,  and 
the  right  hand  figure  in  each  rejected,  and  the  result  will  be 
the  same.  75°,  5  links  or  2  tenths;  lat.  0.52,  dep^l.QS;  carry 
over  the  point,  lat.  .05  ;  dep.  .  19.  65°,  five  links  or  two  tenths, 
lat.  0.85,  dep.  1.81.  lat.  .08,  dep.  .18.  81°,  15  links  orGtenths, 
lat.  0.94,  dep.  5.93;  lat.  .09,  dep.  .59.  28°,  2  links  or  8-100, 
lat.  .07,  dep.  .04.  7°,  15  1.  or  0  tenths,  lat.  60,  dep.  .07. 

What  is  the  latitude  and  departure  on  N.  10°,  E.  6.5  rods? 

This  need  not  be  taken  by  two  inspections,  one  for  the  in- 
teger and  another  for  the  decimal,  but  under  10°,  against  65, 
the  latitude  is  64.01,  and  the  departure  is  11.29. 

The  separating  point  may  be  placed  between  the  two  first 
figures  in  each,  and  as  the  fourth  figure  in  the  departure  is  9, 
a  unit  may  be  added  to  the  third,  the  fourth  figure  in  each 
may  be  omitted,  and  the  latitude  is  6.40  rods,  and  the  depar- 
ture is  1.13  rods. 


PRACTICAL  SURVEYING. 


EXPLANATION  OF  THK  COMPASS,  WITH   DIRECTIONS  HOW  TO 
USE  IT,  AND   HOW  TO   PROVE  THE  ACCURACY  OF  IT. 


In  surveying,  each  angular  point  is  considered  the  centre 
of  a  circle  divided  into  360  equal  parts,  called  degrees. 

The  circle    is  also  divided   into  four  equal  parts,  called 
quadrants,  by  north  and  south,  an'l  east  and  west  lines,  cross- 
ing each  other  at  right  angles  on  the  centre.     Each  quadrant 
is  divided  into  nine  equal  divisions,  and  each  division  con 
tains  ten  degrees. 

The  following  figure  represents  the  card,  or  the  graduation 
of  the  compass. 


APPENDIX. 


93 


At  the  centre  is  the  pivot  or  centre-pin  on  which  the  needle 
turns.  The  compass  is  fixed  on  the  head  of  a  stafTi  and  it 
may  be  directed  to  any  object  on  any  course  whatever, 
while  the  needle  retains  its  polarity.  Courses  are  counted 
either  east  or  west  from  their  respective  meridians.  To  be 
more  explicit,  the  angle  which  a  course  makes  with  its  me- 
ridian, is  written  north  or  south,  so  many  degrees  east  or  west. 

Fix  the  above  circle  to  the  four  cardinal  points,  and  sup- 
pose your  course  runs  from  the  centre  through  the  point  40, 
to  the  right  of  N. ;  the  direction  of  it  is  N.  40°  E..  or  in  the 
opposite  direction  S.  40°  W.  To  take  this  course,  turn  the 
north  end  of  the  compass  to  the  object  at  the  terminating 
point  of  the  line.  This  will  turn  the  point  40  at  the  left  of 
N.  directly  against  the  north  end  of  the  needle,  then  count 
the  degrees  from  N.  to  the  north  end. 

Suppose  your  course  runs  from  the  centre  through  the 
point  80  below  W.,  the  direction  of  it  is  S.  80°  W.,  or  in  the 
opposite  direction  N.  80°  E.  To  take  this  course,  turn  the 
south  end  of  the  compass  to  the  object,  and  the  point  80 
above  W.,  will  be  at  the  north  end  of  the  needle,  and  that  at  80 
below  E.  at  the  south  end  of  it.  In  like  manner  take  all 
other  courses. 

9 


94  APPENDIX. 

In  some  compasses  which  are  sufficiently  correct  for  field 
surveying,  when  one  end  of  the  needle  settles  at  any  degree, 
the  other  end  will  not  settle  exactly  against  the  same  degree 
on  the  opposite  side.  Even  compasses  of  the  first  rate,  when 
they  are  not  well  levelled,  are  liable  to  this  error.  There- 
fore, all  courses  should  be  taken  from  the  same  end  of  the 
needle,  which  may  be  the  north  end.  For  example,  sup- 
pose your  course  is  southeasterly  or  southwesterly,  direct 
the  compass  .to  the  object,  and  at  whatever  degree  the  north 
end  of  the  needle  settles,  enter  it  in  your  field  book,  even 
if  the  south  end  differs  a  few  minutes  from  that  degree. 
Also  keep  the  same  end  of  the  compass  northerly  and 
southerly  on  courses  in  that  direction,  and  the  same  end 
easterly  and  westerly  in  the  latter  direction.* 

By  following  these  directions,  the  survey  will  be  taken 
more  correctly,  than  when  the  ends  of  the  compass  are  fre- 
quently changed,  and  the  northerly  courses  are  taken  by  the 
north  end  of  the  needle,  and  the  southerly  courses  by  the 
south  end  of  it. 

When  a  needle  is  well  magnetized,  the  inside  of  the  cap 
smooth,  and  the  centre-pin  nicely  pointed,  the  needle  will 
traverse  lively  and  long:  but  before  it  stops  at  the  true  point, 
will  have  an  almost  imperceptible  tremulous  motion. 

When  the  needle  settles  quick,  by  giving  the  compass  or 
the  staff  a  light  rap,  ,it  will  commonly  move  a  little,, some- 
times a  quarter,  a  half,  or  a  whole  degree.  This  is  certain 
evidence  that  something  is  out  of  order.  Either  the  needle 
is  not  well  magnetized,  the  inside  of  the  cap  is  rough,  or  the 
centre-pin  is  blunt,  which  causes  friction.  The  centre-pin 
ought  to  be  as  nicely  pointed  as  a  fine  sewing-needle. 
Whether  the  compass  is  in  order  or  not,  the  rap  should  be 
given  after  the  needle  has  settled. 

The  centre-pin  is  the  part  of  a  compass  which  fails  first 
The  point  is  easily  broken  or  blunted,  and  is  always  in  dan- 
ger. When  the  point  is-  injured,  it  is  not  easily  renewed  so 
as  to  be  equal  to  its  first  state.  Therefore,  too  great  care 
cannot  be  taken 'of  a  good  compass. 

When  a  new  compass  is  procured,  it  may  be  recommended 
to  have  one  or  more  extra  centre-pins  with  it,  that  when  one 
fails  another  may  be  in  readiness. 

To  prove  the  accuracy  of  a  compass,  set  each  end  of  it  to 
some  distant  object  at  every  ten  degrees  around  the  circle. 
If,  in  every  instance,  each  end  of  the  needle  settles  at  the 

*  This  practice  has  been  recommended  by  the  most  celebrated  ma- 
thematical instrument  makers. 


APPENDIX.  95 

same  degree  on  the  opposite  side,  the  compass  is  accurate, 
and  is  of  the  first  rate ;  but  if  there  should  be.  found  a  differ- 
ence of -five  minutes  on  a  part  or  around  the  whole  circle,  the 
compass  would  be  considered  as  one  of  the  second  rate,  and 
by  following  the  foregoing  directions,  a  survey  might  be 
taken  with  it  to  a  good  degree  of  accuracy. 

A  compass  which  does  not  come  within  one  or  the  other  of  the 
foregoing  descriptions,  ought  not  to  be  used  on  valuable  land. 

When  a  compass  is  not  in  use,  it  should  be  placed  where 
it  can  have  no  motion,  and  the  needle  should  be  left  oh  the 
centre-pin.  By  keeping  its  polarity,  the  magnetic  power  of 
the  needle  will  strengthen  rather  than  weaken. 

Compasses  differ  in  their  directions.  Those  of  the  first 
rate  have  been  known  to  vary  within  the  space  of  a  quarter 
or  a  third  of  a  degree,  when  no  defect  could  be  discovered  in 
the  mechanical  part  of  them.  As  correct  a  survey  may  be 
taken  with  one  as  with  another  of  this  description.  The  ques- 
tion then  naturally  arises,  which  of  these  varying  compasses  is 
right  ?  The  answer  is,  all  are  right ;  neither  of  them  points 
directly  to  the  poles  of  the  earth,  except  on  the  line  of  no  de- 
clination.* All  that  can  be  said  of  them  is,  that  one  makes  a 
greater  declination  than  another,  and  that  which  makes  the 
least,  cannot  have  the  preference.  It  has  also  been  ascertained, 
that  different  needles  do  not  point  alike  at  the  same  place. 
French  writers  on  magnetism  have  treated  on  this  subject. 

It  was  well  known  to  the  celebrated  Rittenhouse,  that  his 
compasses  did  not  agree,  and  he  was  never  satisfied  as  to  the 
cause  of  it.  To  remedy  this  defect,  if  it  can  be  called  a  defect, 
he  constructed  his  compass  with  a  nonius,  or  vernier  scale,  (as 
some  term  it,)  that  all  of  them  might  be  so  regulated  by  a 
meridian  as  to  agree.  The  meridian  should  be  established  by 
the  motion  of  the  heavenly  bodies,  and  made  permanent  by 
durable  monuments.  All  courses,  which  are  matters  of  re- 
cord, ought  to  be  taken  from  the  true,  instead  of  the  magnetic 
meridian.  Such  meridians  should  be  established  at  conve- 
nient distances  from  each  other,  so  that,  whenever  a  survey  is 
to  be  taken  in  the  vicinity  of  one  of  them,  a  surveyor  might 
set  his  compass  on  it,  and  note  the  declination  found,  and  that 
declination,  together  with  the  meridian  from  which  it  was 
taken,  should  be  inserted  in  the  deed,  or  instrument,  by  which 
the  land  is  conveyed,  and  should  be  a  part  of  the  record.  This 
would  assist  a  surveyor,  at  any  future  period,  in  retracing 
those  lines,  by  setting  his  compass  on  the  same  meridian,  and 

*  As  compasses  differ  in  their  direction,  they  will  differ  in  locating 
this  line. 


96  APPENDIX. 

allowing  the  difference  in  declination  since  the  preceding  sur- 
vey. This  would  tend  greatly  to  the  security  of  landed  prop- 
erty, and  it  is  the  only  method  by  which  magnetic  courses 
can  be  regulated.  Without  this  regulation,  one  correct  com- 
pass may  be  used  to  as  good  advantage  as  another.  So  Dr. 
Rittenhouse  viewed  the  matter :  so  the  common  practice  of  the 
country  has  established  it. 


No.  II. 

ON  THE  IRREGULARITIES  OF  THE  MAGNETIC  NEEDLE. 

By  a  statute  of  this  state,  applicants  for  the  appointment  of 
county  surveyor,  are  required  to  be  well  skilled,  in  point  of 
science,  in  the  theory  of  the  most  approved  method  of  survey- 
ing lands.  It  is  also  as  necessary  that  they  should  be  as  well 
skilled  in  practical  surveying.  Practical  knowledge  must  be 
acquired  by  experience,  but  no  one  can  have  a  thorough 
knowledge  of  correct  practice,  without  being  acquainted  with 
the  imperfections  of  the  magnetic  needle. 

It  is  supposed,  by  most  people,  that  this  instrument,  in  all 
places,  points  directly  to  the  poles  of  the  earth,  and  that  its 
direction  remains  as  permanent  as  the  poles  themselves,  an 
infallible  guide.*  This  is  a  mistaken  idea.  A  few  remarks 
on  this  subject  will  here  be  offered,  and  some  facts  respecting 
it  stated. 

'"  *  Ther^osj3iiaIin£^Liim£dlhe.glial2e  on  which  there  is  no.  declination. 
The  general  course  of  this  line,  on  this  side  of  the  glebe,  is  from  north- 
west to  southeast,  but  it  is  crooked  and  irregular  in  its  course.  This  line 
is  not  stationary,  but  is  ever  changing  its  position,  and  notwithstand- 
ing the  great  variety  of  its  directions,  it  never  crosses  itself.  According 
to  Dr.  Holly's  chart,  made  in  1700,  this  line  crossed  the  meridian  of 
London  in  55°  south  latitude,  crossed  the  equator  in  17°  west  longitude ; 
from  thence  by  various  windings  to  the  island  of  Bermuda;  from 
thence  nearly  a  west  course,  until  it  struck  the  continent  near  Charles- 
ton, in  South  Carolina. 

About  1750,  another  chart  was  made,  when  the  line  had  fallen  so  far 
to  the  west",  that  it  struck  the  continent  near  the  coast  of  Florida.  On 
the  east  side  of  this  line,  the  magnetic  needle  points  to  the  west  of  north, 
and  on  the  west  side,  it  points  to  the  east  of  north,  and  a  regular  increase 
of  either  east  or  west  declination  is  found  from  it  on  its  opposite  sides. 

The  line  of  no  declination  now  runs  through  Pennsylvania,  and 
\  through  the  eastern  part  of  Virginia  and  of  North  Carolina,  and  it 
\leaves  the  coast  at  Cape  Hatteras.t 

*  At  New  Orleans,  in  1813,  the  declination  was  east  about  eight  de- 
grees. The  same  year,  an  article  appeared  in  a  Philadelphia  paper, 
from  which  the  following  was  extracted : 

At  Philadelphia,  "  1701,  declination  8°  30'  W.j  in  1793,  1°  3<y  W.; 

t  Capt.  Phillips. 


APPENDIX.  97 

Notwithstanding  the  utility  of  the  magnetic  needle,  it  cannot 
be  relied  on,  when  great  accuracy  is  required,  on  account  of 
the  irregularities  to  which  it  is  subject,  viz.,  its  annual  and  di- 
urnal variations,  and,  what  is  the  cause  of  still  greater  per- 
plexity, its  local  attractions.  When  an  old  course  is  given  to 
renew  a  line,  it  cannot  be  depended  on,  on  account  of  the 
change  in  declination,  between  the  time  of  the  first  running, 
and  the  renewal  of  it. 

179-1,  the  needle  was  observed  to  recede  to  the  west;  180i,  2°  W. ; 
1813,  23  27/  W. ;"  and  the  west  declination  was  then  increasing.     Ac- 
cording to  observations  made  at  Albany,  by  the  late  M^DeWitt,  Sur- 
veyor General  of  the  State  of  New  York,t  for  mariy^ye^t^^T^TTe'e 
hajLdeclined  to  the  wesL^ 

"^""Observations' made  at  Yale  College,  New  Haven,  and  by  Nathaniel 
Goodwin,  Esq.,  of  Hartford,  agree  with  those  of  the  late  Mr.  De  Witt. 

In  June,  1805,  the  writer  commenced  observing  the  declination  of 
the  magnetic  needle,  at  Hebron,  in  Connecticut,  and  he  has  continued 
his  observations  to  the  present  date,  June.  1835.  The  same  compass, 
with  the  same  needle,  has  been  set  at  the  same  place,  and  to  the  same 
object.  During  that  period,  the  north  end  of  the  needle  declined  to  the 
west  lc  207.  At  the  former  dale,  the  declination  was  4°  50'  W.  The 
annual  motion  of  the  needle  has  not  been  uniformly  steady.  In  some 
years  k  was  more  rapid  than  in  others,  and,  in  one  or  two  instances, 
for  a  period  of  three  or  four  years,  none,  except  the  diurnal  motion, 
could  be  discovered.  The  west  declination  is  still  increasing. 

While  at  so  many  places  in  the  northern  states,  and  at  many  more     • 
which  might  be  mentioned,  the  west  declination  has  increased,  at  Sa- 
lem, in  Massachusetts,  according  to  the  observations  of  Dr.  Bowditch, 
it  has  steadily  decreased. 

In  1580,  at  London,  the  magnetic  needle  pointed  eleven  degrees  and 
a  half  to  the  east  of  north,  which  proves  that  the  line  of  no  declination 
was  then  east  of  that  place. 

The  east  declination  diminished  until  1G57,  when  the  line  of  no  de- 
clination arrived  there,  and  passed  by;  of  course,  west  declination 
commenced,  and  at  the  close  of  the  last  century,  it  had  increased  to 
twenty-four  degrees. 

The  line  of  no  declination  must  have  made  rapid  progress  through 
the  Atlantic,  and  through  a  great  part  of  the  United  States,  to  have  ar-        j 
rived  at  Charleston  in  1700,  and  at  the  coast  of  Florida  in  1756. 

It  is  unaccountable,  how  the  west  declination  at  London  should  in- 
crease, while  at  Philadelphia  it  diminished,  when  both  places  were  on 
the  same  side  of  the  line  of  no  declination. 

The  mystery  is  solved  with  equal  difficulty,  how  the  west  declination  ] 
at  Salem  should  diminish,  while  at  Philadelphia,  Albany,  New  Haven,  • 
and  at  Hartford,  it  increased.  The  declination  of  the  needle  has  long  I 
been  a  subject  of  much  perplexity.  Observations  have  been  made  in  \ 
abundance.  Many  facts  have  been  ascertained,  but  they  are  not  re-  \ 
ducible  to  system. 

The  polarity  of  the  needle,  with  its  variations  and  irregularities,  is 
a  hidden  mystery,  which  is  never  to  be  searched  out  by  man.  It  is 
sufficient  in  i'tself,  without  any  other  evidence,  to  cause  the  reflecting 
mind  to  wonder  at,  admire,  a'nd  adore  the  wisdom,  knowledge,  and 
power  of  HIM,  who  planned,  and  who  still  directs  it 

t  He  died  in  1834. 


98  APPENDIX, 

No  annual  rate  can  be  fixed  on  as  a  certain  rnle  for  the  de- 
clination of  the  needle,  as  its  motion  is  much  more  rapid  in 
some  years  than  in  others.  By  observations  made  at  London, 
during  a  period  of  more  than  two  hundred  years,  it  appears 
that,  in  some  years,  the  motion  of  the  needle  was  rapid,  in 
others,  but  little  could  be  discovered,  and,  in  some  years,  the 
motion  was  retrograde.  There  is  no  regularity  in  its  motion 
at  any  place,  for  any  length  of  time. 

The  diurnal  motion  of  the  needle  has  long  been  known. 
As  the  sun  rises  in  the  forenoon,  it  has  an  effect  on  the  un- 
known something  which  gives  polarity  to  the  needle,  and  turns 
the  north  end  of  it  to  the  west.  In  the  afternoon  and  night 
following,  the  needle  returns  to  its  position.  Observations  for 
the  diurnal  motion  have  been  made  in  abundance,  both  in  Eu- 
rope and  America.  The  result  on  both  continents  has  been 
nearly  the  same.  In  summer,  about  a  sixth  or  a  quarter  of  a 
degree  is  usually  found.  In  winter,  but  very  little  can  be  dis- 
covered. Perhaps,  in  a  hot  climate,  the  diurnal  motion  may 
be  greater. 

Local  attraction  is  found  oftener  in  hilly,  broken  lands,  fill- 
ed with  ledges,  than  in  level,  feasible  land,  where  there  are 
no  ledges.  As  the  sources  of  attraction  are  generally  un- 
known, and  are  out  of  sight,  their  situation  should  be  deter- 
mined by  experiment.  They  sometimes  cause  the  needle  to 
deviate  more  than  a  degree,  and  often  occasion  a  more  trifling 
inaccuracy.  In  some  instances,  differences  have  been  found,  of 
more  than  five  degrees,  within  the  distance  of  forty  rods. 

Although  the  magnetic  needle  is  not  that  infallible  guide 
which  most  people  suppose,  yet  it  is  a  very  useful  instrument, 
and,  in  our  country,  cannot  be  wholly  dispensed  with  in  land 
surveying;  but  the  surveyor  who  is  best  acquainted  with  it, 
will  make  as  little  use  of  it  as  he  can. 


No.  III. 

ON  PRACTICAL  SURVEYING. 

Surveying  is  a  branch  of  business;  which  will  admit  of  dili- 
gence, but  it  will  not  bear  to  be  hurried.  Sufficient  time  must 
be  allowed  to  take  courses,  measure  distances,  and  to  make 
calculations  correctly,  even  if  the  employer  does  not  see  the 
necessity  of  being  so  particular. 

In  taking  a  survey,  go  around  with  the  sun,  or  keep  the 
land  which  you  survey  on  your  right  hand,  not  that  you  can 
work  more  correctly,  or  that  it  will  have  any  effect  in  plot- 


APPENDIX.  99 

ing  or  in  calculating,  but  when  you  put  your  courses  and 
distances  on  your  map,  they  will  follow  around  from  the  left 
to  the  right,  as  you  perform  any  other  writing,  and  your 
map  will  appear  to  better  advantage  than  when  you  write 
against  courses  and  distances. 

Wherever  you  begin,  set  your  compass  on  the  first  angle, 
and  cause  a  stake  or  a  flag-staff  to  be  erected  at  the  next. 

If  the  first  bound  is  a  rock,  erect  a  stake  on  it,  and  set 
your  compass  any  where  between  the  two  stakes,  or  you 
may  go  back  of  the  first  angle,  and  take  the  range  of  the 
stakes. 

When  the  boundary  line  is  not  straight,  place  the  flag  at 
the  first  angle,  and  go  forward  to  a  convenient  place  for  the 
next,  and  take^our  course  by  a  back  sight. 

When  a  line  is  of  such  a  length  that  you  cannot  see  the 
end,  and  do  not  know  the  exact  direction  of  it,  leave  a  flag 
at  the  beginning,  and  go  forward  as  far  as  you  can  have  a 
fair  view  of  it,  and  set  your  compass  to  the  flag.  Pursue 
that  course  to  the  end,  and  if  your  strike  the  bound,  you 
need  not  boast  of  superior  skill,  for  it  will  be  by  accident. 
A  line  run  in  this  manner,  is  commonly  termed  a  random 
line. 

When  the  course  of  a  random  line  is  not  in  a  direction  to 
the  bound,  continue  it  to  a  point  from  which,  by  turning  at  a 
right  angle,  you  will  strike  the  bound,  then  measure  the  dis- 
tance from  the  end  of  the  random  line  to  the  bound,  and  this 
distance  and  the  length  of  the  random  line  will  be  the  legs 
of  a  right  angled  triangle,  the  hypothenuse  of  which  will  be 
the  true  distance,  and  the  bearing  of  the  hypothenuse,  the 
true  course. 

When  the  course  of  a  random  line  is  northwesterly  or 
southeasterly,  and  it  strikes  to  the  right  of  the  bound,  the 
angle  formed  by  the  true  and  the  random  line,  must  be  add- 
ed to  the  course  of  the  latter,  but  if  to  the  left,  it  must  be 
substracted. 

When  the  random  course  is  northeasterly  or  southwester- 
ly, and  it  strikes  to  the  right  of  the  bound,  the  angle  must 
be  substracted,  but  if  to  the  left,  it  must  be  added. 

When  a  line  crosses  a  hill,  cause  a  stake  or  flag  to  be 
erected  at  each  end  of  it,  and  set  your  compass  on  the  top  of 
the  hill,  directly  between  them.  If  bushes  or  a  hedge  ob- 
struct the  sight  on  the  line,  make  an  offset  at  each  end,  or 
take  the  course  by  a  random  line. 

When  a  distant  tree  near  the  line  can  be  seen  at  the  be- 
ginning of  it,  the  bearing  of  the  tree  may  be  taken,  and  the 


100  APPENDIX. 

distance  measured,  and  from  the  tree  to  the  bound,  and  the 
bearing  of  the  bound  from  the  tree,  may  be  taken  by  a  back 
sight,  and  the  course  and  distance  may  be  calculated  by  a 
traverse. 

EXAMPLE. 

Suppose  from  the  beginning  of  a  line,  a  tree  bears  N.  5° 
W.  and  the  distance  is  50  rods ;  from  the  tree  to  the  end  of 
the  line,  is  N.  5°  E.,  50  rods,  the  course  of  the  line  is  north, 
and  the  distance  is  99  rods  and  15^  links. 

When  a  line  crosses  water  which  cannot  be  measured  with 
a  chain,  cause  a  stake  to  be  erected  on  the  opposite  side, 
directly  in  the  line.  Then  turn  from  the  line  at  right  an- 
gles, and  measure  until  the  course  on  which  you  ran  from 
the  line,  and  the  bearing  of  the  stake,  form  an  angle  of  45°, 
then  the  distance  from  the  angle  to  the  point  of  turning  off, 
and  from  that  to  the  stake,  will  be  precisely  the  same,  which 
may  be  added  to  the  distance  already  found. 

If  it  is  not  convenient  to  measure  so  far  as  to  form  an  an- 
gle of  45°,  stop  at  any  proper  distance,  and  take  the  bearing 
of  the  stake,  and  having  ascertained  the  angle,  calculate  the 
distance  across  the  water  by  the  following  proportion.  As 
the  sine  of  the  angle  at  the  stake  :  is  to  its  opposite  side  :  : 
so  is  the  co-sine  of  that  angle  :  to  the  side  required. 

EXAMPLE. 

Suppose  the  bearing  of  the  stake  is  N.  84°  W.,  you  may 
turn  to  the  right  or  to  the  left ;  if  to  the  former,  your  course 
will  be  N.  6°  E.,  and  if  you  measure  16  rods,  and  then  take 
the  bearing  of  the  stake,  which  may  be  S.  74°  W.,  the  angle 
at  the  stake  will  contain  22°.  State  the  question  as  follows  - 
As  sine  of  22°  9.573575 

:  16  rods          -  1.204120 

:  :  co-sine  of  22°  -         9.967166 


11.171286 
Sine  brou  srht  down  -         9.573575 


:  Dist.  across  the  water        -  1.597711       39.6  rods 

If  it  is  not  convenient  to  turn  from  the  line  at  right  angles, 
turn  at  an  acute  or  an  obtuse  angle,  measure  a  suitable  dis- 
tance, take  the  bearing  of  the  stake,  and  calculate  the  dis- 
tance by  oblique  trigonometry. 


APPENDIX.  101 


EXAMPLE. 


Suppose,  on  the  same  line  you  turn  and  run  N.  27°  W.  15 
reds  and  3  links,  the  stake  on  the  opposite  shore  will  bear  S. 
74°  W.  The  angle  at  the  stake  will  contain  22°,  that  at  the 
point  of  turning-  from  the  line,  57°,  of  course  the  other  angle 
will  contain  101°.  In  this  case,  all  the  angles  and  the  side 
opposite  to  that  at  the  stake,  are  given.  The  distance  across 
the  water  may  be  calculated  by  the  first  case  of  oblique  tri- 
gonometry. 

When  a  line  crosses  a  ledge  too  high  and  too  steep  to  be 
measured  with  a  chain,  whether  the  ascent  or  descent  is  be- 
fore you,  erect  #  flag  at  the  top  of  it,  take  a  station  at  the 
bottom,  and  ascertain  the  distance  by  the  method  of  ascer- 
taining it  across  the  -water,  which  will  give  the  base  of  the 
hill  from  your  station  to  a  point  directly  under  the  flag. 

In  taking  courses,  on  account  of  local  attractions,  the  com- 
pass should  be  set  at  least  twice  on  each  line,  even  if  you 
have  a  fair  view  of  the  whole  length  of  it.  Should  there  be 
a  difference  in  the  traverse  of  the  compass  at  the  two  places, 
a  third  should  be  selected.  Should  the  compass  traverse 
alike  at  two  places,  the  surveyor  may  conclude  that  he  has 
found  the  true  course,  but  when  no  two  places  are  found 
where  the  compass  has  the  same  traverse,  the  surveyor  should 
enter  a  medium  course  in  his  field  book,  noting  such  courses, 
as  he  may  still  have  occasion  to  corre'ct  them  in  his  calcu- 
lation. 

If,  in  such  cases,  he  is  at  a  loss  what  course  to  enter  in  his 
field  book,  and  suspects  that  some  minutes  may  be  added  to, 
or  substracted  frorn  the  course  which  he  enters,  he  should 
prefix  to  such  courses  the  sign  of  addition  or  substraction,  as 
the  case  may  be,  which  will  often  assist  him  in  balancing  his 
surveys.  It  would  be  no  easy  matter  to  describe  all  the 
different  methods  which  may  be  selected  in  different  cases 
in  taking  the  field  work  of  surveys.  An  example  of  only 
one  case  will  be  given  here,  which  is  represented  by  the  fol- 
lowing figure. 


102 


APPENDIX. 


\ 


\ 


n 


The  survey  was  be- 
gun at  the  corner  num- 
bered 1.  The  corner 
numbered  2,  was  in  a 
pond.  The  course  and 
distance  were  taken 
from  1  to  m  ;  then  from 
m  to  n.  The  angle  at 
2  was  a  right  angle  ;  of 
course  there  was  a  right  - 
angled  triangle,  where- 
in the  angles  and  hy- 
pothennse  were  given 
to  find  the  sides  m2  and 

2n.     From  n  to  3,  the  >;*< -g''' 

course     and     distance 

were  taken  on  the  line.  The  next  line  ran  through  a  thicket 
in  a  swamp.  Courses  and  distances  were  taken  from  3  to  s, 
thence  to  z,  thence  to  4,  and  the  course  and  distance  of  the 
line  3 — 4  were  calculated  by  a  traverse  from  those  courses 
and  distances.  At  the  angle  5,  a  tree  stood  on  a  high 
clump  of  rocks,  inaccessible  on  either  line  terminating  at 
that  point.  The  course  from  4  to  5  was  taken  at  4.  Next, 
the  course  and  distance  were  taken  from  4  to  a,  and  from  a 
the  course  was  taken  to  5.  Next  the  course  and  distance 
were  taken  from  a  to  6,  and  from  6  the  course  was  taken  to 
5.  Two  oblique  triangles,  with  the  angles  and  one  side  in 
each,  were  given,  to  find  the  side  4 — 5  and  5 — 6,  which  give 
the  base  of  the  hill. 

The  closing  line  ran  through  thick  bushes  and  water,  and 
the  course  and  distance  were  taken  on  the  dotted  line  to  the 
line  1 — 2,  at  a  point  twenty  rods  from  1.  The  course  and 
(distance  of  6 — 1,  were  calculated  accordingly. 

Whenever  a  line  runs  through  or  over  a  place  where  it  is 
difficult  to  take  either  course  or  distance  correctly,  if,  by 
taking  a  traverse  around,  at  a  little  distance  from  the  line, 
the  surveyor  can  have  level,  cleared  land,  and  then  calculate 
the  true  course  and  distance  from  the  courses  and  distances 
of  the  traverse  lines,  he  will  be  more  likely  to  ascertain  the 
correct  course  and  distance,  than  he  would  by  attempting  to 
run  on  the  line.  By  practice  and  experience,  a  method  for 
taking  courses  and  distances,  in  all  cases,  will  become 
familiar. 

In  a  hilly  country,  the  two-pole  chain  is  preferable,  and  is 
more  commonly  used,  because  it  can  be  better  levelled. 


APPENDIX.  103 

In  measuring  hills  arid  inclined  surfaces,  the  horizontal  dis- 
tance must  be  taken.  A  plummet  should  be  suspended  from 
the  end  of  a  chain  when  it  is  levelled. 

When  hills  are  very  steep,  the  surveyor  should  assist  the 
chainmen,  and  when  the  best  is  done  in  levelling  and  plumb- 
ing the  chain,  judgment  must  frequently  be  called  into  exer- 
cise. 

Even  when  elevations  and  descents  are  easy,  there  is  danger 
of  making  too  much  measure.  In  such  cases,  chainmen  often 
make  allowances,  but  the  Surveyor  will  do  better  to  keep  them 
to  close  measure,  and  from  the  shape  of  the  ground,  judge  what 
allowances  ought  to  be  made.  An  experienced,  judicious 
surveyor,  will  form  a  more  correct  judgment  in  such  cases, 
than  inexperienced  men. 

If  a  surveyor  is  acquainted  with  the  rise  or  descent  of  hills, 
the  traverse  table  will  aid  him.  For  example,  from  the  sur- 
face of  a  hill  which  rises  on  an  angle  of  five  degrees,  one  link 
for  every  ten  rods  may  be  deducted. 

Particular  care  must  be  taken  to  have  the  chain  carried  on 
a  straight  line.  When  a  tally  is  ended,  and  the  hinder  chain- 
man  carries  forward  the  sticks,  they  must  be  counted, 
When  on  counting  the  sticks  it  is  discovered  that  one  is  lost, 
the  chainmen  should  not  leave  the  chain  and  go  back  to  find 
it,  but,  from  the  last  mark,  should  measure  back  to  the  point 
where  the  tally  commenced,  to  see  whether  the  full  tally  was 
measured,  or  whether  one  chain  was  lost  from  it.  Many 
blunders  have  been  left  undetected  by  not  taking  this  care. 
A  careful,  accurate  chainman,  never  loses  a  stick,  or  miscounts 
a  tally. 

Distances  may  be  taken  by  chains  and  Jinks,  or  by  rods  and 
decimal  parts,  as  best  suits  the  surveyor.  When  a  survey  is 
calculated  by  chains  and  links,  the  numbers  by  which  the 
process  is  performed,  are  smaller  than  when  it  is  calculated 
by  rods  and  decimal  parts.  Every  method  by  which  the 
numbers  are  diminished,  is  an  improvement. 

Young  surveyors  should  practice  much  for  their  own  in- 
struction, and  should  make  correct  practice  familiar,  before 
they  offer  their  services. 

A  young  surveyor  should  bear  in  mind,  that  if  he  is  detected 
in  one  error  in  the  beginning  of  his  practice,  it  will  be  more 
to  his  disadvantage  than  to  be  detected  in  two,  when  he  shall 
become  well  established.  If  an  error  is  committed  in  a  sur- 
vey, it  is  not  against  the  surveyor,  provided  he  detects  and 
corrects  it ;  but  if  he  cannot  do  this,  it  is  sufficient  evidence  of 
Jus  deficiency  in  point  of  knowledge  and  skill. 


104  APPENDIX. 

No.  IV. 

DIRECTIONS  FOR  RUNNING  AND  ESTABLISHING  LINES. 

Many  people  suppose  that  a  surveyor,  at  the  beginning  of 
a  line,  by  intuition,  or  by  some  magic  art,  can  set  his  compass 
directly  to  the  terminating  point,  whatever  obstructions  may 
intervene,  and  that  he  needs  no  assistance ;  but  this  is  a  mis- 
taken idea. 

In  running  a  line  of  considerable  length,  a  surveyor  should 
have  two  assistants  to  carry  the  chain,  two  to  carry  flags,  in 
whose  ability  and  correctness  he  can  confide,  and  a  fifth  to 
carry  an  axe.  If  the  surveyor  is  not  furnished  with  such  a 
number  of  assistants,  his  employer  need  not  place  too  much 
confidence  in  his  work, 

The  flag  staves  should  be  as  much  as  two  and  a  half  or 
three  inches  in  diameter,  or  what  would  be  better,  two  strips 
of  a  board  of  that  width,  and  seven  or  eight  feet  in  length.  If 
they  are  not  so  wide,  they  cannot  be  seen  through  the  sights 
of  the  compass  at  any  great  distance.  On  one  end  of  each 
staff,  a  flag,  either  white  or  red,  of  a  yard  in  length,  should 
be  wound  tight,  and  not  left  to  hang  loose  and  flutter  in  the 
wind.  The  latter  colour  will  be-  more  clearly  seen  through 
bushes,  especially  when  the  ground  is  covered  with  .snow, 
and  the  brighter  the  colour  the  better.  Being  thus  manned 
and  equipped,  at  the  beginning  of  a  line,  he  must  set  his  com- 
pass as  near  the  true  line  as  he  can,  or,  he  may  set  up  one  of 
the  fjags  at  the  place  of  beginning,  and  go  forward  as  far  as 
he  can  have  a  view  of  the  back  flag.  There  set  his  compass 
on  the  random  line,  and  send  the  other  assistant  as  far  for- 
ward as  he  can  conveniently  see  the  flag.  When  each  flag 
is  clearly  seen  through  the  sights  of  the  compass,  the  back 
flag  must  be  brought  forward,  a'nd  placed  wrhere  the  compass 
stood.  In  this  manner  he  must  proceed  on  his  random  line, 
taking  care  each  time  he  sets  his  compass,  to  turn  the  sights 
to  the  back  flag.  Great  care  must  be  taken  to  keep  the  flags 
perpendicular;  also,  the  surveyor  must  keep  the  staff  and  the 
sights  of  the  compass  perpendicular.  A  little  leaning  of  the 
flags,  or  turning  the  sights  of  the  compass  from  a  perpen- 
dicular, will  make  a  crooked  line.  In  taking  his  sights  to 
the  flags,  he  must  look  as  near  the  ground  as  he  can,  and 
when  practicable,  the  flag  should  be  turned  downwards,  on 
account  of  the  danger  of  being  leaned  when  kept  up. 

All  obstructions,  such  as  bushes,  brush,  &c.,  must  be  cleared 
away.  The  random  line  must  be  measured,  and  at  con- 


APPENDIX.  105 

lenient  distances,  perhaps  at  every  twenty  rods,  stakes  must 
be  set  directly  in  it.  Every  stake  must  be  numbered,  that  no 
mistake  may  be  made  in  calculating,  when  they  are  after- 
wards removed  arid  placed  on  the  true  line.  If,  in  the  course 
of  the  random  line,  the  needle  does  not  traverse  as  at  first,  or 
does  not  traverse  alike  at  different  places,  no  regard  should 
be  paid  to  it,  the  flags  must  direct  the  course;  neither  should 
the  surveyor  be  turned  aside  or  terrified  by  the  cry  of  either 
of  the  parties,  you  are  wrong,  you,  are  wrong,  (for  he  will 
most  certainly  hear  it,)  bathe  must  continue  his  random  line, 
until,  turning  at  right  angles,  either  to  the  right  or  to  the  left, 
as  the  case  may  be,  he  can  exactly  strike  the  bound,  or  the 
point  where  a  bound  is  to  be  erected ;  there  he  may  stop,  and 
measure  the  distance  from  that  place  to  the  bound.  He  may 
then  calculate  the  course  and  distance  of  the  true  line,  as  be- 
fore taught ;  but  for  setting  the  stakes  in  the  true  line,  he  may 
take  the  following  directions. 

Suppose  the  whole  length  of  the  random  line  is  200  rods, 
and  the  distance  from  the  termination  of  it  to  the  bound  is  90 
links,  the  calculation  for  setting  the  stakes  on  the  true  line 
may  be  made  thus: — As  the  whole  distance  :  is  to  90  links 
:  :  so  is  the  distance  of  any  stake  :  to  the  distance  that  such 
stake  is  to  be  moved. 

If  the  stakes  are  20  rods  apart,  the  answer  is,  the  first  stake 
is  to  be  moved  nine  links,  the  second  18  links,  and  so  on,  add- 
ing nine  links  at  each  stake,  until  the  whole  are  moved  at 
right  angles  from  the  random  to  the  true  line.  Many  crooked 
lines  and  consequent  disputes  between  farmers,  have  arisen 
from  the  want  of  this  care  and  attention.  When  a  long  line 
is  to  be  run  over  a  number  of  ridges,  and  across  intervening 
valleys,  it  should  first  be  run  and  established  from  one  ridge 
to  another,  and  the  intermediate  spaces  in  the  valleys  may  be 
taken  afterwards.  By  taking  long  sights,  there  will  be  less 
danger  of  turning  from  a  straight  line. 

In  all  cases,  the  forward  flag  should  be  carried  as  far  as  it 
can  be  distinctly  seen,  unless  it  is  at  the  termination  of  a 
line. 

On  account  of  the  irregularity  of  the  magnetic  needle,  the 
difference  between  compasses,  and  the  incorrect  manner  in 
which  most  of  the  former  surveys  were  made,  no  rule  can  be 
given  which  may  be  relied  on,  with  certainty,  in  renewing 
lost  bounds.  In  such  cases,  the  best  evidence  must  be  taken 
which  can,  be  produced.  When  an  old  line  is  to  be  renewed, 
where  the  bounds  have  ""been  "lost,  the  surveyor  may  verify  or 
prove  his  accuracy  in  various  modes.  If  he  finds,  for  exam- 
ple, that  the  lots  on  each  side  of  the  line  contain  their  due 


106  APPENDIX. 

quantity,  or  possess  their  full  width,  he  will  have  reason  to 
believe  that  the  line  is  accurately  run;  if  not,  he  may  allow 
for  the  excess  or  deficiency  in  either  of  these  lots,  and  thus 
discover  the  true  position  of  the  line. 

It  would  be  difficult  to  mention  all  the  circumstances  which 
may  govern,  or  which  may  serve  as  evidence  in  such  cases. 


No.  V. 

ON  BALANCING   SURVEYS. 

In  every  survey  which  is  taken  without  an  error,  either  in 
courses  or  in  distances,  the  sum  of  the  northings  will  equal 
that  of  the  southings;  and  the  sum  of  the  eastings  that  of  the 
westings;  but  this  is  not  always  an  infallible  proof  that  the 
survey  is  accurate,  for  two  errors  may  be  committed,  one  of 
which  will  exactly  balance  the  other,  which  no  rule  will  de- 
tect; but  such  cases  do  not  often  occur. 

In  practical  surveying,  it  is  next  to  an  impossibility,  in  any 
case,  to  work  so  correctly  that  the  survey  will  exactly  close 
without  some  correction.  The  difference  between  the  two 
columns  of  latitude,  and  between  those  of  departure,  are  the 
legs  of  a  right  angled  triangle,  the  hypothenuse  of  which  will 
be  the  distance  which  the  survey  will  fail  of  closing.  In  a 
survey  of  one  hundred  acres,  whatever  may  be  the  number 
of  the  angles,  the  difference  between  the  two  columns  of  lati- 
tude, and  the  two  columns  of  departure,  ought  not  to  exceed  a 
rod  for  each,  but  to  come  within  those  limits,  if  possible. 

If,  in  such  a  survey,  either  of  the  differences  should  exceed 
a  rod,  where  the  land  is  valuable  and  easily  surveyed,  it 
would  be  better  to  take  a  re-survey,  or  so  far  as  to  detect  the 
error.  ' 

These  differences,  as  before  taught  in  this  work,  must  be 
balanced  before  the  column  of  meridian  distances  can  be 
formed,  or  a  correct  plot  of  the  survey  be  drawn. 

The  small  differences  between  the  columns  in  surveys 
which  are  substantially  correct,  commonly  arise  from  an  ex- 
cess of  measure,  on  account  of- the  irregularity  of  surface,  and 
from  errors  of  the  compass,  caused  by  local  attraction,  and 
diurnal  motion. 

Some  authors  have  given  rules  for  balancing  surveys,  which, 
in  theory,  appear  plausible,  but,  in  practice,  they  are  not  with 
out  exceptions.*  In  correction,  these  rules  are  indiscrimi- 
nately applied  to  every  line  in  the  survey,  which  pre- 

*  It  is  argued,  by  theorists,  that  by  these  rules  all  will  be  agreed.  This 
is  admitted, 'but  then,  all  may  be  agreed  in  error. 


APPENDIX.  107 

supposes  that  a  proportional  error  must  have  been  commit- 
ted on  each  and  all,  both  in  courses  and  in  distances ;  when 
in  almost  every  survey,  a  part  of  the  lines  are  on  land  so 
level  and  so  clear  from  obstructions  of  any  kind,  that  if  the 
surveyor  and  chainmen  attend  to  their  business,  they  will  not 
be  likely  to  commit  much  error  on  them,  while  other  lines 
on  other  parts  of  the  same  survey  are  attended  with  so  many 
difficulties,  that  when  they  have  done  their  best,  it  will 
scarcely  be  possible  for  them  to  avoid  some  error,  and  the 
surveyor  who  takes  the  survey  will  best  judge  on  what 
lines  the  errors  were  committed,  and  whether  they  were  in 
the  courses  or  in  the  distances.  In  all  cases,  the  corrections 
should  be  made  on  the  lines  containing  the  errors. 

When  the  errors  are  in  the  courses,  they  should  be  cor- 
rected, and  when  the  errors  are  in  the  distances,  the  correc- 
tion should  be  in  them,  or  the  correction  may  be  in  both 
courses  and  distances,  as  the  surveyor  may  judge  proper. 

Surveys  are  commonly  balanced  by  substracting  half  the 
sum  of  the  differences,  from  the  numbers  in  the  larger  col- 
umns, and  by  adding  them  to  those  in  the  less. 

This,  in  most  instances,  is  a  correct  method,  but  in  certain 
cases,  there  are  exceptions  to  it.  For  example,  the  bounda- 
ry lines  of  three  sides  of  a  farm  are  on  level  land  where  there 
are  no  obstructions.  The  other  side  is  on  rough  land  rilled 
with  broken  precipices.  In  such  a  case,  most,  if  not  all  the 
correction,  should  be  on  the  lines  on  the  rough  side.  In 
some  instances,  most  of  the  error  may  be  in  the  course  of  a 
single  long  line. 

It  is  not  uncommon  on  high  hills  that  the  traverse  of  the 
needle  differs  a  quarter  or  half  of  a  degree,  or  more,  from  its 
traverse  in  valleys  and  on  plains  below.  In  such  cases, 
courses  should  be  corrected.  In  general,  the  compass  is 
subject  to  more  error  than  the  chain.  As  rules  cannot  be 
given  for  correcting  surveys  in  all  cases,  this  must  be  left  in  a 
great  measure  to  the  judgment  and  experience  of  the  surveyor. 

As  a  general  rule,  corrections  should  be  made  principally 
on  long  lines,  and  the  correction  may  be  in  proportion  to 
the  difficulties  with  which  the  surveying  of  them  is  attended. 

When  a  course  is  north  or  south,"  or  east  or  west,  or  near 
either  of  those  points,  a  few  minutes  may  be  added  to  it  or 
substracted  from  it,  when  necessary  to  favour  the  balancing.  If 
the  distance  is  of  considerable  length,  it  is  probable  that  the 
course  may  contain  some  error. 

When  a  course  is  nearly  equidistant  between  any  two  of 
the  four  cardinal  points,  if  the  correction  of  it  increases  the 
latitude  and  diminishes  the  departure,  or  if  it  diminishes  the 


108 


APPENDIX. 


latitude  and  increases  the  departure,  so  as  to  favour  the  balan- 
cing, there  is  double  evidence  that  the  course  contains  some 
error.  If  by  diminishing  the  distance  on  such  a  course,  both 
the  latitude  and  departure  are  so  diminished  as  to  favour  the 
balancing,  it  is  good  evidence  of  an  excess  of  measure. 

In  correcting  surveys,  there  is  less  danger  from  diminishing 
distances  than  there  is  from  increasing  them.  Cases  may 
occur  in  which  distances  may  be  increased,  but  the  surveyor 
should  be  very  cautious  about  it. 

As  it  is  of  importance  that  surveys  should  be  correctly  bal- 
anced before  they  are  calculated,  and  as  the  work  is  commonly 
attended  with  some  difficulty,  a  few  examples  are  given  for 
the  assistance  of  the  student.  In  each  survey,  the  courses  and 
distances  are  entered  in  the  tables  as  they  were  taken  in  the  field. 

EXAMPLE    I. 


r 

Courses. 

Dist. 
rods. 

N. 

S. 

E. 

W. 

1 

N.  40°  30'  W. 

53.0 

40.30 
.20 

34.42 
.53 

2 

N.  10  15  E. 

74.4 

73.21 
.00 

13.24 

3 

S.  85  30  E. 

125.5 

9.85 
10.25 

125.11 

4 

S.    7  15  W. 

71.8 

71.22 
.32 

v 

9.06 

5 

S.    2  15  E. 

31.2 

31.18 

.28 

1.23 

6 

N.  84  00  W. 

35.5 

3.71 
.50 

* 

35.31 

7 

W. 

40.0 

.10 

40.00! 

8 

S.  80  00  W. 

21.0 

3.65 
.75 

20.68 

117.22 

115.90 

139.58 

139.47 

Balanced, 

116.70 

1  1,6.70 

139.58 

139.58 

APPENDIX. 


109 


The  difference  betweett  the  sum  of  the  northings  and  that 
of  the  southings  is  one  rod  and  8  links,  and  the  difference  be- 
tween the  sum  of  the  eastings  and  that  of  the  westings  is 
2f  links*  The  taking  of  the  course  on  the  third  line  was 
attended  with  difficulty,  and  probably  it  contains  some  error, 
therefore,  more  than  a  proportion  of  the  correction  is  made 
on  the  southing  of  it.  There  is  also  evidence  that  the  first 
course  contains  some  error,  as  the  diminishing-  of  the  north- 
ing and  the  increasing  of  the  westing  favours  the  balancing. 
Twenty  links  are  added  to  the  different  southings,  and  thir- 
teen links  are  substracted  from  the  different  northings 

Where  corrections  are  made,  the  upper  numbers  are  of  no 
further  use.  If  the  corrections  are  made  with  red  ink,  they 
will  all  be  seen  at  one  view,  and  the  work  will  appear  hand.- 
This  was  Mr.  Flint's  practice. 


sorrier. 


EXAMPLE  II. 


2 

£ 

Courses. 

Dist. 
rods. 

N. 

S. 

E. 

W. 

i 

N.  5°  00'  E. 

44,4 

44.23 

3,86 
.75 

2 

E. 

66.6 

.22 

66.60 
.40 

3 

N.  20  00  E. 

22.6 

-21.23 

7.72 

4 

S.  80  00  E. 

59.0 

10.25 
.10 

58.10 
,00 

5 

S.  8  15  W. 

57.0 

56.41 
.30 

8.18 
.33 

6 

N.  85  30  W. 

41.4 

3.25 
.40 

41.27 
.39 

7 

S.  45  00  W. 

28.5 

20.15 

20.15 

8 

S.  7  00  E. 

24.4 

24.22 

2.97 
,90 

9 

S.  80  15  W. 

38.2 

6.47 
.35 

37.65 

10 

W. 

20.4 

20.40 

11 

N.  12  30  W. 

49.2 

48.04 

10.65 
.85 

1230 

116.75 

117.50 

139.25 

138.30 

1        Balanced, 

117.12  117.12 

138,77 

138.77 

10* 


HO 


APPENDIX. 


EXAMPLE    III. 


2 

p 

Courses. 

Dist. 
Rods. 

N. 

S. 

E. 

W. 

1 

N.  20°  00'  W. 

70.0 

65.78 

23.94 
24.05 

2 

N.  12  30  W. 

45.4 

44.32 

9.83 

3 

N.  10  00  E. 

38.5 

37.91 

6.69 

4 

N.  15  00  W. 

38.0 

36.71 

9.84 

5 

N.  86  00  E. 

80.8 

5.65 
.75 

80.61 
.51 

6 

S.  88  00  E. 

65.2 

2.27 
.18 

65.16 
.06 

7 

N.  84  30  E. 

72.0 

6.90 
700 

71.67 
.57 

8 

S.     5  45  E. 

100.0 

99.50 
.30 

10.02 

9 

W. 

71.6 

.18 

71.60 

10 

S. 

88.6 

88.60 
.50 

.20 

a 

N.  87  00  W. 

50.2 

2.63 
.73 

50.13 

12 

S.  81  15  W. 

69.0 

10.50 
.40 

68.20 

199.90 

200.87 

234  15 

233.54 

Balanced, 

200.38 

200.38 

233.85 

233.85 

In  the  correction  of  the  two  last  surveys,  the  differences 
between  the  two  columns  of  latitude,  and  between  those  of 
departure,  in  each  example,  are  equally  divided  between 
their  respective  columns.  A  northing  is  added  to  the  second 
course  in  the  second  example ;  also,  a  northing  to  the  ninth, 
and  a  westing  to  the  tenth,  in  the  third  example.  When 
courses  are  entered  in  the  field  book,  north,  south,  east,  or 
west,  they  are  as  liable  to  contain  errors,  and  they  are  as 
subject  to  correction,  as  other  courses. 


APPENDIX. 
EXAMPLE  IV. 


Ill 


No. 

Courses. 

Dist. 

rods. 

N. 

S. 

E. 

W. 

1 

N.  7°  45'  E. 

41.8 

41.42 

5.64 

2 

.20 

.58 

S.  79  00  E. 

47.0 

8.97 

46.14 

9.15 

3 

N.  40  00  E. 

25.0 

19.15 

16.07 

.00 

4 

S.  70  00  E. 

60.0 

20.52 

56.38 

.72 

5 

S.  15  00  E. 

15.6 

15.07 

4.06 

6 

N.  89  00  E. 

57.0 

.99 

56.99 

.80 

7 

S.     3  30  E. 

96.5 

96.32 

5.89 

.76 

8 

S.  87  45  W. 

174.6 

6.86 

174.46 

7.20 

9 

N.    2  15  E. 

84.2 

84.14 

3.31 

.00 



.18 

10 

N.  80  00  W. 

20.0 

3.47 

19.70 

.46 

1 

149.17 

147.74 

194.48 

194.16 

Balanced, 

148.46 

148.46 

194.16 

In  the  last  example,  the  difference  between  the  northings 
and  the  southings  is  equally  divided. 

As  it  was  judged  that  sufficient  distances  were  made  on  the 
two  westerly  courses,  the  correction  was  made  on  the  east- 
ings. 


112  APPENDIX. 

No.  IV. 
ON  RECTANGULAR  SURVEYING. 

Rectangular  surveying*  is  a  name  given  to  the  method 
here  treated  of  by  the  late  Governor  Treadwell. 

In  the  operation  of  it  the  whole  survey  is  reduced  to 
squares  and  parallelograms,  and  each  of  these  figures  is  di- 
vided into  two  right  angled  triangles  of  equal  shape,  or 
into  two  trapezoids  of  equal  size  and  shape,  by  a  boundary 
line  of  the  field  running  obliquely  through  it,  except  when 
the  boundary  line  is  directly  north  and  south,  then  the  figure 
is  divided  into  two  squares  or  parallelograms. 

The  calculations  are  made  from  a  meridian  drawn  either 
at  the  eastern  or  at  the  western  extremity  of  the  map ;  and 
the  areas  are  produced  by  multiplying  the  latitudes  by  the 
longitudes  made  from  this  meridian. 

All  the  spaces  lying  between  the  field  and  the  meridian, 
and  between  the  parallels  of  latitude  of  the  northern  and 
southern  extremities  of  it,  also  large  spaces  lying  without 
the  figure  on  the  opposite  side  of  it,  and  between  those  par- 
allels, are  included  in  the  calculation ;  but  that  which  lies 
without,  is  eventually  excluded. 

Parallels  of  latitude  are  drawn  from  each  angle  to  the 
meridian,  which  are  called  meridian  distances. 

In  forming  the  column  of  meridian  distances,  when  the 
meridian  is  drawn  at  the  eastern  extremity,  the  westings  are 
added,  and  the  eastings  substracted  ;  but  when  the  meridian  is 
laid  on  the  west  side,  the  eastings  are  added  and  the  westings 
substracted. 

The  meridian  distances  proceeding  from  each  end  of  a  line 
are  added  together,  to  form  the  column  of  double  mean  dis- 
tances, which  the  compiler  of  the  foregoing  work  called  se- 
cond departure. 

Meridian  distances  and  double  mean  distances,!  are  more 
proper  terms  or  names  for  these  columns,  than  first  departure 
and  second  departure. 

The  meaning  of  the  term  meridian  distance,  is  the  distance 
made  from  any  meridian. 

The  following  survey  is  calculated  from  the  meridian  of 

*  Rectangular  calculation  is  as  proper. 

t  The  compiler  of  the  foregoing  work  would  have  made  use  of 
these  names,  but  he  was  afraid  of  infringing  on  a  certain  copy-right 
which  has  expired. 


APPENDIX. 


113 


the  first  station  which  is  on  the  west  side  of  the  figure,  of 
course,  the  eastings  are  added  and  the  westings  substracted. 
The  whole  is  illustrated  by  this  figure. 


114 


APPENDIX. 


To  form  the  first  column  marked  at  the  top  Merid.  Dist.  set 
the  easting  of  the  first  line  16.90,  into  the  head  of  the  column, 
which  is  the  meridian  distance  of  2,  or  the  distance  from  2  to 
s.  To  this  number,  add  the  easting  of  the  second  line,  and 
their  sum  is  22. 11,  the  meridian  distance  of  3,  or  the  distance 
from  3  to  n.  To  this  number  add  the  easting  of  the  third 


APPENDIX.  US 

line,  and  their  sum  is  80.07,  the  meridian  distance  of  4,  or  the 
distance  from  4  to  m.  From  this  number,  substract  the 
westing  of  the  fourth  line,  and  73.82  remains,  the  meridian 
distance  of  5,  or  the  distance  from  5  to  a.  From  this  num- 
ber, substract  the  westing  of  the  fifth  line,  and  70.33  remains, 
the  meridian  distance  of  6,  or  the  distance  from  6  to  z.  From 
this  number,  substract  the  westing  of  the  closing  line,  and 
00.00  remains,  which  proves  the  work  correct  so  far.  When 
the  last  substraction  does  not  end  in  a  cipher,  an  error  has 
been  committed  somewhere. 

In  forming  the  column  of  double  mean  distances,  take  the 
following  directions  : — • 

Add  together  two  opposite  sides  of  each  figure  formed  by 
the  meridian  distances.  Set  the  first  meridian  distance  into 
the  head  of  the  next  column,  or  that  marked  at  the  top  D. 
M.  D.,  and  it  gives  one  side  of  the  parallelogram  Is — 2c. 
This  figure  is  divided  into  two  equal  triangles  by  the  line 
1 — 2.  The  meridian  distance  multiplied  by  the  northing  of 
the  line  1 — 2,  gives  the  area  of  the  whole  parallelogram,  or 
the  double  area  of  one  of  the  triangles.  Let  this  be  consid- 
ered, that  which  lies  without  the  field.  -To  the  line  2s,  add 
3ft,  and  their  sum  is  39.01,  the  length  of  the  parallelogram 
nxos,  which  is  divided  into  two  equal  trapezoids  by  the  line 
2 — 3.  The  double  mean  distance  39.01,  multiplied  by  the 
northing  of  the  line  2 — 3,  gives  the  area  of  the  parallelogram, 
or  the  double  area  of  one  of  the  trapezoids. 

Let  this  be  considered  that  which  lies  without  the  field. 

To  the  line  3w,  add  4?rc,  and  their  sum  is  102.18,  the 
length  of  the  parallelogram  mien,  which  is  divided  into  two 
equal  trapezoids  by  the  line  3 — 4.  The  double  mean  distance 
102. 18,  multiplied  by  the  northing  of  the  line  3 — 4,.  gives 
the  area  of  the  parallelogram,  or  the  double  area  of  one  of 
the  trapezoids.  Let  this  be  that  which  lies  without  the  field. 
To  the  line  4m,  add  50,  and  their  sum  is  153.89,  the  length 
of  the  parallelogram  mdfa,  which  is  equally  divided  by  the 
line  4 — 5.  The  double  mean  distance  153.89,  multiplied  by 
the  southing  of  the  line  4 — -5,  gives  the  area  of  the  parallelo- 
gram, or  the  double  area  of  one  of  the  trapezoids. 

Let  this  be  that  which  abuts  on  the  meridian,  being  partly 
within  and  partly  without  the  field. 

To  the  line  5a,  add  62,  and  their  sum  is  144.15,  the  length 
of  the  parallelogram  auvz,  which  is  equally  divided  by  the 
line  5 — 6.  The  double  mean  distance  144.15,  multiplied  by 
the  southing  of  the  line  5 — 6,  gives  the  area  of  the  parallelo- 
gram, or  the  double  area  of  one  of  the  trapezoids.  Let  this 


116  APPENDIX, 

be  a5 — 6jz,  partly  within  and  partly  without  the  field.  To 
the  line  6z,  nothing  is  to  be  added,  of  course,  it  is  one  side 
of  the  parallelogam  z6~—wl,  which  is  equally  divided  by  the 
closing  line.  The  distance  70.33,  multiplied  by  the  southing 
of  the  closing,  line,  gives  the  double  area  of  the  triangle 
zQ — 1,  partly  within  and  partly  without  the  field. 

The  three  products  in  the  column  of  north  areas,  all  lie 
without  the  field.  Those  in  the  column  of  south  areas  lie 
partly  within  and  partly  without  the  field,  and  they  include 
all  the  space  which  is  covered  by  the  products  in  the  column 
of  north  areas. 

Hence  it  is  plain,  that  when  the  sum  of  the  former  is  sub' 
stracted  from  that  of  the  latter,  the  double  area  of  the  field 
will  remain.  In  this  method,  when  the  column  of  meridian 
distances  and  that  of  double  mean  distances  are  correct,  the 
sum  of  the  latter  will  be  double  to  that  of  the  former. 

PENNSYLVANIA  METHOD. 

If  the  writer  has  been  correctly  informed,  this  improvement 
was  made  by  Dr.  Rittenhouse. 

Only  one  column  is  used  for  meridian  distances,  but  the 
final  results  are  the  same  as  when  two  columns  are  used. 

This  method  is  not  so  easily  explained  to  the  learner,  but 
is  perhaps  preferable  in  practice,  because  an  error  may  be 
committed  in  forming  the  column  of  double  mean  distances, 
which  may  not  be  discovered ;  but  in  this  method,  an  error 
cannot  be  committed  in  the  meridian  distances,  \vithout  being 
detected.  A  full  explanation  of  this  method  would  be  tedious 
and  perplexing  to  the  learner,  without  being  of  the  least  use 
in  performing  practical  operations,  and  probably,  if  made, 
but  little  attention  would  be  paid  to  it ;  therefore,  only  direc- 
tions how  to  form  the  column,  and  how  to  apply  the  numbers 
in  their  practical  use,  will  be  given. 

The  operation  of  this  method  is  substantially  the  same  as 
that  of  the  other,  and  the  diagram  given  in  that  will  answer 
for  this.  The  north  and  south  products  are  precisely  the 
same  in  both  methods.  A  further  investigation  of  this  method 
will  be  left  for  the  learner  when  he  shall  be  more  expe* 
rienced. 

When  the  two  columns  in  the  other  method  are  proved  by 
addition,  the  process  is  longer  than  in  this. 

The  second  column  in  the  foregoing  example,  marked  at 
the  top,  meridian  distances,  is  the  method  here  treated  of. 

To  form  the  column,  add  twice  or  subslract  twice  against 


APPENDIX. 


nr 


each  station.  Set  the  first  easting  16.90  into  the  head  of  the 
column  at  the  upper  place.  Add  it  to  itself,  and  the  sum  is 
33.80  in  the  lower  place.  To  this  number  add  the  next  east- 
ing, and  they  make  39.01  in  the  upper  place.  To  this  num- 
ber add  the  same  easting  again,  and  they  make  44.22  in  the 
lower  place.  To  this  number  add  the  third  easting,  and  they 
make  102.18  in  the  upper  place.  To  this  number  add  the 
same  easting  again,  and  they  make  160.14  in  the  lower 
place. 

From  this  number  substract  the  first  westing,  and  153.89 
remains  in  the  upper  place.  From  this  number  substract  the 
same  westing  again,  and  147.64  remains  in  the  lower  place. 

From  this  number  substract  the  second  westing,  and  144.15 
remains  in  the  upper  place.  From  this  number  substract  the 
same  westing  again,  and  140.66  remains  in  the  lower  place. 
From  this  number  substract  the  last  westing,  and  70.33  re- 
mains in  the  upper  place. 

From  this  number  substract  the  same  westing  again,  and 
00.00  remains.  The  upper  number  against  each  station  in 
this  column,  is  the  same  as  the  double  mean  distance  which 
stands  against  it ;  and  the  remainder  of  the  process  may  be 
performed  •  as  before  directed.  Another  column  may  be 
formed  as  the  eleventh  in  this  example,  marked  H.  D.  at  the 
top,  which,  for  distinction,  is  here  called  half  distance.  It 
contains  half  the  sum  of  the  numbers  in  the  double  mean 
column.  These  numbers,  when  multiplied  by  their  respective 
northings  or  southings,  give  the  simple  areas  of  the  different 
figures. 

This  method  is  preferable  in  practice,  as  the  multiplica- 
tions are  greatly  diminished.  When  the  last  decimal  in  the 
double  mean  distances  is  an  odd  number,  a  unit  may  be  taken 
off,  and  take  half  the  remainder,  rather  than  annex  another 
decimal :  perhaps  this  would  not  make  the  difference  of  a 
rod  in  a  survey  of  three  hundred  acres.  Or  the  odd  num- 
bers in  the  last  place  of  decimals  may  be  balanced  by  some- 
times adding  a  unit. 

If  the  numbers  are  diminished  a  trifle,  it  may  be  remarked, 
that,  on  account  of  uneven  surfaces,  there  is  danger  of 
making  the  distances  too  much,  rather  than  falling  short  of 
the  true  measure.  There  are  other  methods  by  which  sur- 
veys may  be  calculated  arithmetically,  but  none  are  more 
correct,  and  perhaps  none  are  so  simple  and  so  easy  to  be 
understood  as  the  methods  here  treated  of.  These  methods 
may  be  applied  in  every  case  in  practical  surveying,  which 
depends  on  a  calculation  from  courses  and  distances. 

11 


118 


APPENDIX. 


Instead  of  laying  the  meridian  on  one  side,  it  may  be  laid 
through  the  map,  either  at  an  angle,  or  so  as  to  bisect  a  boun- 
dary line ;  but  this  renders  the  process  more  complex  and 
difficult. 


PENNSYLVANIA  METHOD. 


This  example  is  calculated  by  chains  and  links. 


55 
p 

1 

2 

Courses. 

Dist. 

N. 

S. 
1.08 

E. 

W. 

M.dist. 
164.06 

1391580 

S.88°15'  W. 

35.25 

35.23 
.21 

45.57 
.54 

128.85 
93.64 

S.  86  30  W. 

45.65 

2.79 

48.10 
02.56 

225990 

3 

N.  2  15  W. 

32.55 

32.53 

1.28 

1.28 
0.00 

416384 

4 

N.  87  00  E. 

20.25 

1.06 

20.22 

20.22 
40.44 

212332 

5 
6 

7 
8 

N.  3  00  W. 

25.40 

25.37 
3.40 

62.36 

25.47 

33.04 
.02 

62.38 

59.90 

1.33 

39.11 

37.78 

9922207 



N.  86  45  E. 

60.00 
25.50 

97.68 

157.58 

3321120 

S.  2  45  E. 

1.22 
2.02 
83.36 

158.80 
160.02 

40446360 

53505608 

S.  3  30  E. 

33.10 

83.41 

162.04 
164.06 

13872043  '95569538 
1387-2043 

181697495 

408.48747 
4 

1.94988 

40 

37.99520 

1 

A.    a.    Rods. 

408     1      38.  38 

The  above  survey  was  commenced  and  terminated  at  the 
southeast  corner.  Against  the  fourth  station,  the  addition  of 
the  eastings  in  the  column  of  meridian  distances  begins,  and 
the  substraction  of  the  westings  terminates  directly  over  it. 


APPENDIX.  119 

The  lower  number  against  the  8th  station  is  164.06.  This 
is  placed  over  the  head  of  the  column,  and  the  three  first 
westings  are  substracted  from  it. 

If  the  fourth  course  had  been  placed  against  the  first  num- 
ber, and  the  others  had  followed  in  succession,  the  addition 
would  have  began  at  the  head  of  the  column,  and  the  sub- 
straction  would  have  ended  at  the  bottom,  and  the  result  would 
have  been  the  same.  Perhaps  this  may  be  a  better  method 
for  the  student,  and  for  the  young  surveyor,  but  one  who  is 
experienced  can  derive  no  benefit  from  it. 


No.  VII. 


ON  PLOTTING  SURVEYS. 

Surveys  may  be  plotted  by  various^  methods.  That  which 
is  commonly  practised,  is  by  a  scale  and  protractor. 

The  latter  instrument  is  a  semicircle,  graduated  like  the 
compass,  and  it  answers  the  same  purpose  in  laying  angles  on 
paper,  that  the  compass  does  in  taking  them  in  the  field. 

A  meridian  is  drawn  for  each  station  or  angle  in  the  sur- 
vey, and  the  angle  which  each  course  makes,  with  its  respect- 
ive meridian,  is  laid  down  with  the  protractor,  and  each  dis- 
tance by  a  scale  of  even  parts.  It  would  be  well  also  to  draw 
a  parallel  of  latitude  for  each  station,  as  by  such  parallels  the 
protractor  may  be  kept  more  truly  to  the  meridians. 

A  plot  may  be  drawn  by  laying  down  the  angles  by  the 
protractor  without  meridians  or  parallels  of  latitude,  as  has 
already  been  taught  in  the  foregoing  work ;  but  the  writer 
never  had  so  good  success  by  this  method  as  he  has  had  by 
laying  his  courses  from  meridians. 

As  the  scale  and  protractor  are  equally  subject  to  error,  the 
surveyor  will  be  more  likely  to  draw  a  correct  plot  if  he 
should  dispense  with  the  latter  instrument,  and  lay  down  the 
boundary  lines  from  the  latitude  and  departure  of  each,  or 
from  the  latitude  and  meridian  distance  of  each  station. 

To  plot  from  the  several  latitudes  and  departures,  take  the 
foregoing  survey  for  an  example.* 

As  that  survey  is  small,  take  half  a  sheet  of  paper,  and  draw 
meridians  across  each  end  of  it. 

On  the  left  hand  meridian,  make  a  point  for  the  beginning. 
From  that  point  draw  a  parallel  of  latitude  to  intersect  the 
other  meridian,  perpendicular  to,  or  at  right  angles  with 
each. 

*  Page  114. 


120  APPENDIX, 

The  latitude  of  the  first  course  is  36.25.  Draw  another 
parallel  of  latitude  at  that  distance  above  the  first. 

The  latitude  of  the  second  course  is  29.54.  This,  added  to 
the  first,  makes  65.79.  Draw  another  parallel  at  this  distance 
above  the  first. 

To  the  sum  of  the  first  and  second  latitudes,  add  that  of  the 
third,  and  their  sum  is  81.32.  At  this  distance  above  the  first, 
draw  another  parallel.  The  southing-  of  "the  fourth  course  is 
35.54.  Substract  this  from  the  whole  sum  of  the  northings, 
and  45.87  remains.  At  this  distance  above  the  first,  draw 
another  parallel.  From  the  last  remainder,  substract  the 
southing  of  the  fifth  course,  and  6.02  remains,  which  is  the 
southing  of  the  closing  line.  At  this  distance  above  the  first, 
draw  the  last  parallel.  In  like  manner,  draw  the  meridian  of 
each  station,  according  to  the  departure  made  en  each  course. 
The  intersection  of  these  lines  will  be  the  angles  of  the  figure. 
If  the  distances  shall  not  exactly  fall  into  these  points,  the  pro- 
cess will  contain  some  error,  either  in  drafting,  or  from  a  scale 
not  accurately  divided. 


TO  PLOT  FROM  LATITUDES  AND  MERIDIAN  DISTANCES. 

First,  form  the  column  of  meridian  distances.  Next  draw 
the  meridian  of  the  first  station,  and  the  several  parallels  of 
latitude,  as  before  directed.  On  these  parallels,  lay  the  me- 
ridian distance  of  each  station,  viz. — from  s  to  2,  16.90;  from 
n  to. 3,  22.11 ;  from  m  to  4,  80.07  ;  from  a  to  5,  73.82;  from 
z  to  6,  70.33. 

From  one  of  these  points  to  another  draw  the  boundary 
lines.  Great  care  must  be  taken  to  keep  the  latitudes  parallel 
and  perpendicular  to  the  meridian.  The  scale  must  be  cor- 
rectly divided,  the  dividers  nicely  pointed,  and  the  rule  must 
be  straight.  Whether  the  protractor  is  used  or  not,  before  a 
plot  of  a  survey  is  drawn,  it  should  be  balanced,  and  both 
courses  and  distances  corrected  according  to  the  balancing. 

The  following  example  is  given  as  a  proof  of  the  necessity 
of  balancing  a  survey  before  the  map  is  drawn. 

A  farm  is  to  be  divided  among  a  number  of  heirs.  A  sur- 
vey of  it  is  taken,  and  the  difference  between  the  two  columns 
of  latitude  and  those  of  departure,  is  two  rods  for  each.  The 
survey  is  balanced  and  calculated  arithmetically,  and  is  found 
to  contain  two  hundred  acres. 


APPENDIX.  121 

The  surveyor  next  draws  his  map,  by  which  the  divisions 
are  to  be  made,  according  to  the  courses  and  distances  as 
they  were  taken  on  the  ground.  The  plan  does  not  close 
by  nearly  two  rods  and  three  quarters.  He  next  corrects 
the  lines,  and  maks  the  map  close  as  well  as  he  can  ;.  and 
when  the  divisions  are  made,  they  may  not  agree  with  the 
first  calculation,  by  two  or  three  acres,  or  more.  Should  the 
map  be  drawn  as  before  directed,  by  the  latitudes  and  de- 
partures as  balanced,  or  by  the  latitudes  as  balanced,  and  the 
meridian  distances,  it  would -close,  and  would  be  in  exact 
conformity  to  the  calculation  made  arithmetically.  If  the 
divisions  are  made  arithmetically,  the  calculations  must  be 
made  according  to  the  balancing,  or  the  divisions  will  not 
agree  with  the  first  calculation. 

When  a  map  of  a  multangular  piece  of  land,  of  very  ir- 
regular shape,  is  to  be  drawn,  whether  a  calculation  or  a 
division  is  to  be  made  from  it,  the  surveyor  should  measure 
across  the  lot  between  two  opposite  angles  in  some  central 
place,  at  least  once,  and  in  more  places,  if  convenient,  and 
the  case  requires  it.  By  cross  measures,  the  map  may 
be  more  correctly  drawn,  and  the  divisions  should  be  calcula- 
ted separately.  In  such  cases,  the  surveyor  will  be  more 
likely  to  ascertain  the  true  contents,  than  he  would  by  sur- 
veying only  the  boundary  lines,  and  then  calculating  the  whole 
together. 


No.  VIIL 

ON  DIVIDING  LAND. 

As  lands  are  divided  into  so  great  a  variety  of  shapes, 
rules  cannot  be  given  which  will  answer  in  all  cases. 

In  distributions  of  estates,  the  divisions  are  commonly 
made  with  scale  and  dividers.  This  method  will  answer 
well,  provided  the  map  is  drawn  on  a  large  scale,  which 
should  not  be  less  than  ten  rods  to  an  inch. 

As  more  confidence  can  be  placed  in  arithmetical  calcula- 
tions, it  may  be  recommended  to  every  surveyor  to  make  as 
little  use  of  the  scale  and  dividers  as  he  can ;  but  in  our 
country,  they  cannot,  in  all  eases,  be  dispensed  with. 

In  dividing  lands,  it  will  be  acknowledged  by  every  expe- 
rienced surveyor,  that  it  is  a  difficult  matter  to  make   the 
amount  of  a  considerable  number  of  divisions  agree  with 
the  whole,  when  calculated  by  itsel£ 
11* 


122  APPENDIX. 

A  few  examples  by  arithmetical  calculation  will  be  given. 
Let  the  preceding  figure  be  divided  into  two  equal  parts  by 
a  line  running  eastward  from  the  second  angle.  At  what 
point  on  the  eastern  boundary  will  it  terminate? 

As  you  do  not  know  the  point,  first  calculate  the  area  of 
that  part  which  lies  above  a  line  from  2  to  5. 

Set  the  courses  and  distances  of  the  second,  third,  and 
fourth  courses,  into  their  respective  columns,  having  a  blank 
line  for  the  course,  distance,  latitude,  departure,  &c.  of  the 
closing  line  from  5  to  2.  On  the  two  first  of  these  courses, 
the  sum  of  the  northings  is  45.07  rods,  and  that  of  the  east- 
ing is  63.17  rods,  and  the  course  from  4  to  5  contains  35.45 
rods  of  southing  and  6.25  rods  of  westing.  The  southing 
and  westing  of  the  latter  being  substracted  from  the  north- 
ings and  eastings  of  the  two  former,  leaves  a  balance  of 
9.62  rods  of  southing  and  56.92  rods  of  westing  to  fill  the 
blank  line.  The  latitude  and  departure  of  the  closing  line 
being  given,  the  course  may  be  found  by  the  following  pro- 
portion. 

As  the  latitude  is  to  radius  ;  so  is  the  departure  to  the  tan- 
gent of  the  course.     Look  in  the  column  of  tangents  for  the 
course.     The  course  being  found,  the  distance  may  be  found 
as  follows.     As  the  sine  of  the  course  is  to  the  departure 
so  is  radius  to  the  distance.     See  them  worked. 

Latitude  9.62,  and  the  departure  56.92,  given  to  find  the 
course  and  distance. 

Lat.  9.62  -         -         -  0.983175 

:  radius  -         -       10.000000 

:  :  departure  56.92    -  1.755265 


radius  and  dep.  added  -         -       11.755265 
lat.  brought  down  0.983175 


:  tangent  of  the  course  80°  25'  10.772090 

sine  of  80°  25'          -         -         -.  9.993896 

:  departure  56.92       -  1.755265 

:  :  radius           ....  10.000000 


11.755265 
9.993896 

:  distance         -          57.72  1.761369 

The  course  from  5  to  2  is  S.  80°  25'  W.,  and  the  distance 
is  57.72  rods.     This  being  ascertained,  the  contents  of  that 


APPENDIX.  123 

part  of  the  figure  above  this  line  will  be  found,  eleven  acres 
and  thirty-four  rods,  leaving  a  deficiency  of  one  acre  and  a 
half,  and  thirty-three  rods,  of  making  one  half  of  the  whole 
figure. 

This  quantity  is  to  be  Jaid  in  a  triangle  on  the  line  from  2 
to  5,  and  on  that  from  5  to  G,  running  to  a  point  at  2. 

The  question  is,  what  distance  from  5  towards  6,  will  be 
required  to  give  the  contents  of  the  triangle  ?  To  answer 
such  a  question,  the  area,  the  contained  angle,  and  one  side 
of  the  triangle  must  be  given,  to  find  the  length  of  the  con- 
tiguous side,  including  the  angle.  Having  these  data,  take 
the  following  rule. 

To  the  sine  of  the  given  angle,  or  to  its  supplement  if 
obtuse,  add  the  logarithm  of  the  given  side ;  substract  radius 
from  this  sum,  and  substract  the  remainder  from  the  logarithm 
of  the  double  area :  the  last  remainder  will  be  the  logarithm 
of  the  side  required.  In  this  case,  the  angle  formed  by  the 
line  from  5  to  2,  and  by  that  from  5  to  6,  contains  75°  25', 
the  given  side  is  57.72  rods,  the  area  of  the  triangle  is  273 
rods,  and  the  double  area  is  546  rods.  See  the  rule  worked. 

Sine  of  75^  25'  9.985778 

logarithm  of  the  given  side  57.72      1.761369 

cancel  the  first  figure,  and  R.  is        

substracted  -     1,1.747147 

logarithm  of  the  double  area  -         -.        -         2.737193 

remainder  brought  down          ....         1.747147 


logarithm  of  the  side  required  9.77  rods  0.990046 

Measure  from  5  towards  6,  9  rods  and  19^-  links  to  a 
beech  tree,  from  thence  on  a  straight  line  to  2,  and  the  figure 
will  be  equally  divided.  The  true  position  of  the  divisional 
line  being  established,  the  course  and  distance  of  it  may  be 
calculated  as  before  directed. 

The  course  and  distance  from  2  to  5  are  N.  80°  25'  E. 
57.72  rods  :  from  5  to  the  beech  tree,  S.  5°  W.,  9.77  rods. 
On  the  first,  9.62  rods  of  northing  and  56.92  of  easting  are 
made.  On  the  second,  9.74  rods  of  southing  and  .85  of  a 
rod  of  westing  are  made. 

The  northing  of  the  first  course  being  substracted  from  the 
southing  of  the  second,  and  the  westing  of  the  second  from 
the  easting  of  the  first,  .12  of  a  rod  of  northing,  and  56.07 
rods  of  westing,  are  given  as  data  by  which  the  course  and 
distance  from  the  beech  tree  to  2  may  be  calculated.  The 
course  is  N.  89°  53'  W.,  and  the  distance  is  56.07  rods. 


124  APPENDIX. 

Suppose  it  is  next  required  to  lay  out  15  rods  in  width  be- 
low and  parallel  with  the  dividing  line. 

As  the  eastern  and  western  boundary  lines  both  turn  ob- 
liquely from  the  dividing  line,  the  question  is,  what  distance 
will  be  required  on  each  to  give  the  required  width  ? 

Make  the  distance  on  each  boundary  line  the  hypothenuse 
of  a  right  angled  triangle,  and  15  rods,  the  width  required, 
one  of  the  legs  or  the  base.  The  angle  at  2,  formed  by  the 
boundary  and  dividing  lines,  contains  114°  53'.  Substract 
90°  from  this,  and  24°  53'  remains,  being  the  angle  formed 
by  the  given  leg  (15)  and  the  hypothenuse. 

Take  the  following  proportion  to  find  the  hypothenuse. 

As  the  co-sine  of  24°  53';  is  to  15,  the  given  side;  so  is 
radius  to  the  distance  required.  See  it  worked. 

Co-sine  of  24°  53'         -  9.957687 

:  given  side  15  rods       -  1.176091 

:  :  radius  -         -         -         -       10. 


11.176091 

9.957687 

:  side  required  16.54  rods      -  1.218404 

The  dividing  line  and  the  eastern  boundary,  at  the  beech 
tree,  form  an  angle  of  85°  7'.  Substract  this  from  90°,  and 
4°  53'  remains,  being  the  angle  by  which  the  east  side  must 
be  worked. 

Co-sine  of  4°  53'  9.998421 

:  given  side  15  rods       -                  -         1.176091 
:  :  radius 10. 


11.176091 
9.998421 

:  side  required  15.05  rods       -  1.177670 

The  distances  required  are  15  rods  \\  link  on  the  east- 
ern, and  16  rods  13^  links  on  the  western  boundary. 

Measure  from  2  towards  1,  16  rods  13£  links  to  a  spruce 
tree,  and  from  the  beech  tree  towards  6,  15  rods  11  link  to 
a  pine  tree,  and  calculate  the  distance  from  the  pine  to  the 
spruce,  and  the  division  will  be  completed.  This  calcula- 
tion must  be  made  by  a  traverse  from  the  courses  and  distan- 
ces already  known. 

From  the  spruce  to  2,  N.  25°  E.  16.54  rods ;  from  2  to  the 
beech,  S.  89°  53'  E.  56.07  rods;  from  the  beech  to  the  pine 
S.  5°  W.  15.05  rods.  Arrange  these  courses  and  distances 


APPENDIX. 


125 


in  their  proper  columns  as  follows,  and  calculate  the  latitude 
and  departure  of  each,  having  a  blank  line  for  the  last. 


Courses. 

Dist. 

N. 

S. 

E. 

W. 

N.  25°  00'  E. 

16.54 

14.99 

6.98 

S.  89°  53'  E. 

56.07 

.12 

56.07 

S.    5°  00'  W. 

15.05 

14.99 

1.31 

.12 

61.74 

15.11 

15.11 

63.05 

63.05 

Having  calculated  the  latitudes  and  departures,  substract 
the  northing  of  the  first  course  from  the  sum  of  the  south- 
ings of  the  two  last,  and  .12  of  a  rod  'remains  to  be  entered 
in  the  blank  column  of  northings;  also,  substract  the  westing 
of  the  third  from  the  sum  of  the  eastings  of  the  two  first, 
and  61.74  remains  to  fill  the  blank  column  of  westings. 
This  balance  of  northing  and  of  westing  is  the  latitude  and 
departure  of  the  line  from  the  pine  to  the  spruce.  The  dis- 
tance is  61.74  rods,  and  the  course  agrees  with  that  on  the 
opposite  side. 

Suppose  it  is  next  required  to  lay  out  four  acres  adjoining 
and  parallel  with  the  line  from  the  pine  to  the  spruce. 

As  the  rrgure  of  this  division  is  not  regular,  no  rule  can  be 
given  by  which  it  can  be  calculated  by  one  operation,  but  it 
must  be  done  by  approximation.  - 

Reduce  the  quantity  of  the  division  to  rods,  and  divide  that 
sum  by  the  length  of  the  known  side,  and  the  quotient  will 
be  10.36  rods,  but  as  the  south  side  will  be  longer  than  the 
north,  the  width  cannot  be  so  much. 

Assume  10  rods  as  the  width,  and  calculate  the  distance 
on  each  end  by  the  same  process  that  you  did  those  on  the 
last.  The  angles  in  this  are  the  same  as  in  that. 

Co-sine  of  24°  53'      -         -  9.957687 

:  given  side  10  rods     -         -  1.000000 

:  :  radius  -         -         -  10. 


side  required  11.03  rods 


11.000000 
9.957687 

1.042313 


126 


APPENDIX. 


Co-sine  of  4°  53' 
:  given  side  10  rods 
:  :  radius 


9.998421 
1.000000 
10. 

11.000000 
9.998421 


:  side  required  10.04  rods  1.001579 

The  distances  required  are  10  rods  1  link  on  the  east,  and 

1 1  rods  f  of  a  link  on  the  west  boundary. 

Measure  from  the  spruce  towards  1,  11   rods  f  of  a  link 

to  a  hemlock,  and  from  the  pine  towards  6,  10  rods  1  link  to 

a  maple,  and  calculate  the  distance  from  the  latter  tree  to  the 

hemlock. 

From  the  hemlock  to  the  spruce  N.  25°  E.   11.03  rods; 

from  the  spruce  to  the  pine,  S.  89°  53'  E.  61.74  rods;  from 

the  pine  to  the  maple  S.  5°  W.  10.04  rods. 


Courses. 

Dist. 

N. 

S. 

E. 

W. 

N.  25°  00'  E. 

11.03 

10.00 

4.66 

S.  89°  53'  E. 

61.74 

.12J61.74 

.87 

S.  5°  00'  W. 

10.04 

10.00 

.12 

65.53 

10.12 

10.12 

66.40 

66.40 

The  northing  and  westing  in  the  blank  line  is  the  latitude 
and  departure  of  the  line  from  the  maple  to  the  hemlock. 
The  distance  required  is  65.53  rods.  To  this  distance,  add 
that  of  the  north  side,  and  the  sum  of  both  is  127.27  rods. 
Multiply  half  of  this  sum  by  JO  rods,  the  width  of  the  divi- 
sion as  it  now  stands,  and  the  product  is  636.3  rods.  Sub- 
stract  this  from  640,  and  3.7  rods  remain,  being  a  deficiency. 
To  this  deficiency  annex  three  ciphers,  and  divide  that  sum 
by  the  distance  from  the  maple  to  the  hemlock,  and  the  quo- 
tient will  be  nearly  6,  which  is  .06  of  a  rod,  or  U  link.  To 
the  quantity  already  found,  add  this  width  on  the  south  side, 
and  the  division  will  be  completed. 

The  south  division  of  the  whole  figure  contains  twelve 
acres,  three  quarters,  and  twenty-seven  rods.  This  division, 
now  stands  in  three  subdivisions. 


APPENDIX. 


127 


The  first  contains  five  acres,  two  quarters  ana  three  rods ; 
the  second,  four  acres,  and  if  the  foregoing  calculations  are 
correct,  the  third  contains  three  acres,  one  quarter,  and  twen- 
ty-four rods.  See  the  work  proved. 

There  now  remains  between  the  southeast  corner  and  the 
last  subdivision,  5.08  rods,  and  between  the  southwest  corner 
and  the  same  division,  12.37  rods,  to  be  calculated  on. 


Courses. 

Dist. 

N. 

S. 

E. 

W. 

Me  rid. 
Dist. 

North. 
Areas. 

South. 
Areas. 

S.  5°  00'  W. 

5.08 

5.06 

.45 

141.11 

140.66 

714.0166 

S.  85  05  W. 

70.48 

6.02 

70.33 

70.33 
00.00 

423.3866 

N.  25  00  E. 

12.37 

11.21 

5.23 

5.23 
10.46 

58.6283 

.13 

65.55 

76.01 
141.56 

9.8813 

11.21 

11.21 

70.78 

70.78 

58.6283 

1147.2845 

160 


58.6283 
11088.6562 
k544Y~ 

UsoA3 

64 


A.    dr.    Rods. 
CONTENTS  3       1        24 


No.  IX. 
ON  BOUNDS  AND  ROADS. 

As  the  magnetic  needle  cannot  be  relied  on  in  renewing 
lost  boundaries,  it  is  of  the  first  importance  that  good,  sub- 
stantial bounds,  be  kept  up.  In  divisions,  or  distributions  of 
lands,  surveyors  ought  to  see  that  such  bounds  are  erected. 
It  is  their  business  to  cause  them  to  be  made,  and  such 
bounds  ought  to  be  described  in  deeds,  or  in  the  instruments 
by  which  lands  are  conveyed,  and  to  be  a  part  of  the  record. 
By  proper  care  and  attention  to  this  part  of  the  business, 
many  disputes  may  be  prevented. 

Highways  are  attended  with  more  difficulties  of  this  kind, 


128  APPENDIX. 

than  the  location  of  the  divisions  of  real  estate.  In  laying 
highways,  it  is  the  common  practice  to  lay  the  centre  lines, 
and  order  the  roads  to  be  of  a  certain  width,  and  stakes  are 
usually  set  at  the  angles.  Care  is  not  often  taken  to  set 
bounds  -on  the  sides,  and  when  the  roads  are  made  the  cen- 
tre bounds  are  destroyed,  and  the  travelling  path  is  often 
built  on  one  side  of  the  centre ;  but  as  the  bounds  are  lost, 
it  is  utterly  impossible,  after  a  few  years  have  elapsed,  to 
ascertain  by  the  survey  where  the  road  was  laid. 

Surveyors  who  are  employed  on  such  business  ought  to  de- 
scribe the  angles,  or  as  many  as  is  practicable,  in  such  a 
manner  that  the  road  may  afterwards  be  found. 

It  taking  surveys  of  roads,  the  distance  on  each  proprie- 
tor's land  must  be  noted,  for  the  purpose  of  assessing  dam- 
ages; but  these  distances  need  not  be  entered  in  the  record. 
The  whole  distance  on  each  course  must  be  entered  in  the 
record,  and  it  is  no  matter  whether  it  crosses  the  land  of  one 
or  of  ten  different  owners. 

The  following,  being  a  resurvey  of  a  part  of  the  New 
London  and  Lyme  turnpike  road,  as  was  recently  taken,  is 
prepared  for  record,  and  it  may  serve  as  an  example. 

As  there  is  no  object  of  sufficient  permanency  directly 
against  the  point  of  the  beginning  of  said  road,  it  may  be 
found  by  the  following  direction. 

From  a  point,  35  links  northerly  of  the  northwest  -corner 
of  B.  Brown's  stone  house,  in  the  range  of  the  west  side,  run 
(as  the  magnetic  needle  now  points*)  S.  66°  25'  W.  1 
chain  56  links  to  the  centre  of  a  stone  set  in  the  ground  be- 
neath the  surface,  which  is  the  point  of  beginning  of  said 
road — thence,  on  the  same  course  (S.  66°  25'  W.)  4  chains 
60  links,  to  a  point  49  £•  links  northerly  of  the  northwest 
corner  of  G.  Jones'  store,  in  the  range  of  the  west  side ; 
thence  S.  79°  25'  W.  1 1  chains  52  links  to  a  point  48  links 
northerly  of  the  northeast  corner  of  the  Norris  house,  in  the 
range  of  the  east  side;  thence  S.  80°  10'  W.  17  chains  29 
links  to  a  point  50  links  northerly  of  the  northeast  corner  of 
the  Chester  house,  in  the  range  of  the  east  side.  The  line 
described  by  the  foregoing  survey,  is  the  centre  of  the  road 
which  is  four  rods  in  width. 

An  angle  in  a  road  may  be  described  by  its  bearing  and 
distance  from  some  permanent  object,  such  as  the  corner  of 
a  building,  the  centre  of  a  well,  a  point  of  a  rock,  a  tree,  &c. 
In  cases  where  no  permanent  object  is  near  an  angle,  the 
side  bounds  ought  to  be  set  before  the  Committee  or  Com- 

*  June,  1835. 


APPENDIX,  129 

missioners,  (as  they  may  be  named)  proceed  any  further  in 
the  location  of  the  road. 

When  the  centre  line  of  a  road  is  laid,  the  distance  which 
it  runs  on  any  proprietor's  land  may  be  multiplied  by  the 
width  of  the  road,  and  the  product  will  be  the  quantity  of  land 
taken. 

Whether  the  centre  or  a  side  of  a  road  is  laid,  the  lines  al- 
most uniformly  cross  the  boundary  lines  of  lots  of  land  in 
such  oblique  directions,  that  if  a  side  is  laid,  it  will  require 
too  much  time  to  ascertain  the  exact  quantities  of  land,  which 
will  be  taken  from  different  proprietors. 

Other  advantages  will  be  found  by  laying  the  centre  line  of 
a  road,  which  need  not  here  be  mentioned. 

DIRECTIONS  FOR  TAKING  MINUTES  ON  A  ROAD. 

rods,  links. 

S.  11°  15'  E.  17         00  on  W.  H.'s  land. 
+  30         00  on  R.  S.'s 

-f  89         00  on  T.  B.'s 

f  1£       00  rod  on  old  road. 

Whole  distance  L37i 


No.   X. 

ON  DISTRIBUTING  ESTATES. 

As  the  distribution  of  estates  is  connected  with  surveying, 
something  on  that  subject  may,  with  propriety,  be  added  to 
this  work. 

Surveyors  are  agreed  that  written  distributions  of  real 
estate  are  often,  and  too  often,  returned  to  Courts,  accepted 
and  recorded,  which  are  so  unintelligible  that  it  is  extremely 
difficult  and  sometimes  impossible  to  ascertain,  with  any  de- 
gree of  certainty,  where  the  divisions  of  land  were  originally 
made. 

In  distributing  estates,  surveyors  have  the  minutes,  and  it 
properly  belongs  to  them  to  write  the  distributions. 

To  young  learners  who  are  coming  forward  to  take  an  ac- 
tive part  in  this  business,  some  directions  may  be  given. 

The  divisions  of  land  among  heirs,  in  most  cases,  are  first 
made  on  paper.  When  these  are  completed  and  agreed  to 
12 


130  APPENDIX. 

by  the  distributors,  erect  the  bounds  between  the  several 
divisions.  Next,  from  the  map  on  which  the  divisions  were 
made,  which  will  be  full  of  marks,  and  perhaps  some  blots, 
copy  a  neat  handsome  map  on  new  paper,  noting  thereon  all 
the  courses  and  distances,  and  all  the  bounds,  which  should 
be  entered  in  the  distribution.  Also,  note  in  each  division 
of  the  map  the  quantity  of  land  it  contains,  with  the  name  of 
the  heir  to  whom  it  was  distributed  This  map  is  to  be  kept 
by  the  heirs.  Next  write  the  distribution,  and  before  it 
shall  be  returned  to  Court,  see  that  the  heirs  have  a  copy 
of  it. 

With  a  map  and  a  copy  of  the  distribution,  the  heirs  will 
have  a  record  in  their  own  house,  from  which,  at  any  future 
period,  they  may  find  the  divisions  of  their  land. 

The  following  form  of  a  distribution  has  been  approved 
by  experienced  Judges*  of  Probate  Courts. 

To  the  Honourable   Court  of  Probate  for  the  District  of 
Rockingham. 

The  undersigned,  distributors  of  the  estate  of  BENJAMIN 
BANISTER,  Esquire,  late  of  Applebury,  within  said  district, 
deceased,  have  distributed  said  estate,  under  oath,  as  fol- 
lows : 

To  PHILURA  BANISTER,  widow  of  said  deceased,  as  her 
right  of  dower  in  said  estate,  fifty  acres  of  land  lying  on  the 
front  of  the  farm,  bounded  as  follows: — Beginning  at  the 
northwest  corner  of  said  farm  by  the  highway,  thence  run- 
ning east  by  Roderick  Random's  land,  50  rods  to  a  maple 
tree,  thence  south  parallel  with  the  highway  160  rods  to  a 
hemlock  tree  by  Thomas  Trunnion's  land,  thence  west  by 
said  Trunnion's  land  50  rods  to  the  highway,  thence  north 
by  said  highway  160  rods  to  the  place  of  beginning.  Also, 
the  following  parts  of  the  dwelling  house  [describe  the  parts.] 
Also,  the  following  parts  of  the  barn  [describe  the  parts,  and 
of  other  buildings.] 

PERSONAL  ESTATE. 

Scott's  Bible,  $15.  Bed,  curtains,  &c.  $45.     Look- 
ing glass,  $15.  -  -  $75.00 

To  BENJAMIN  B.  BANISTER,  the  north  division  of  the 
farm,  containing  one  hundred  acres,  being  partly  encumber- 
ed by  dower,  bounded  as  follows  : — Beginning  at  the  north- 

*  Called  Surrogates  in  some  states. 


APPENDIX.  131 

west  corner  of  said  farm,  thence  running  east  by  Roderick 
Random's  lands  200  rods,  to  a  beech  tree  by  Oliver  Gulliver's 
land,  thence  south  by  said  Gulliver's  land,  80  rods  to  a 
spruce  tree,  thence  west  by  land  set  to  Matilda  Banister,  par- 
allel with  said  Random's  land,  200  rods  to  a  white  pine  tree 
by  the  highway,  thence  north  by  said  highway,  80  rods  to  the 
place  of  beginning. 

Also,  one  undivided  half  of  all  the  buildings  belonging  to 
said  estate,  being  partly  encumbered  by  dower. 

Said  division  of  real  estate  is  appraised  at       -       $2500.00 

PERSONAL  ESTATE. 

One  horse,  $100.     Two  yoke  of  oxen,  $130.     Ox 
wagon,  $50.  •  $280.00 

To  MATILDA  BANISTER,  the  south  division  of  the  farm, 
being  the  remainder  and  residue  of  said  farm,  containing  one 
hundred  acres,  and  is  80  rods  in  width  from  front  to  rear, 
being  partly  encumbered  by  dower,  bounded  as  follows  : — 
North  on  the  division  set  to  Benjamin  B.  Banister,  south  on 
Thomas  Trunnion's  land,  east  on  Oliver  Gulliver's  land, 
west  on  highway. 

Also,  one  undivided  half  of  all  the  buildings  belonging  to 
said  estate,  subject,  in  part,  to  incumbrance. 

Said  division  of  real  estate  is  appraised  at       -       $2500.00 

PERSONAL  ESTATE. 

Bed,  curtains,  &c.  $45.     Mahogany  table,  $12.        

Set  of  silver  spoons,  $18  $75.00 

Said  widow  and  said  heirs  have  equal  privileges  of  passing 
to  and  from  any  and  every  part  of  the  real  estate  .set  to  each 
of  them  in  the  foregoing  distribution,  at  the  usual  passways, 
such  as  doors,  stairs,  gates,  bars,  lanes,  paths,  &c. 

HUGH  HUNTER, 
CHARLES  CHALKER.  ' 
Applebury,  July  30^,  1832.      CHRISTOPHER  CUTLER. 

The  foregoing  caption  or  preamble  is  sufficient,  as  it  will 
appear  of  record  that  the  distributors  were  appointed.  Forms 
of  distribution  must  vary  according  to  circumstances. 


No.  XL 
ON  LEVELLING. 

It  is  not  expected  that  land  surveyors  will  qualify  them- 


132 


APPENDIX. 


selves  for  civil  engineers,  or  that  they  will  furnish  themselves 
with  suitable  instruments  for  that  business,  but  every  survey- 
or should  furnish  himself  with, an  instrument  with  which  he 
can  take  levels  and  angles  of  elevation*  or  depression,  with 
a  sufficient  degree  of  accuracy  to  answer  in  cases  of  locating 
roads,  of  ascertaining  whether  water  may  be  carried  in  an 
aqueduct  from  one  place  to  another,  and  to  ascertain  the  fall 
of  mill  seats ;  also,  to  answer  in  all  common  cases.  A  cheap, 
simply  constructed  instrument,  represented  by  the  following 
figure,  is  recommended 


Let  A  B  be  a  strip  of  a  board  three  inches  wide  and  three 
feet  in  length,  or  longer  if  necessary,  made  perfectly  straight 
on  the  top.  The  perpendicular  piece,  which  is  dove- 
tailed into  the  top,  should  be  of  such  a  width  at  the  bottom 
that  it  may  be  graduated  either  way  from  the  centre,  ten  or 
fifteen  degrees ;  and  of  such  a  length  that  the  radius  by  which 
the  graduated  arch  is  swept,  should  be  at  least  a  foot.  Great 
care  must  be  taken  in  the  graduation,  to  have  it  done  cor- 
rectly, and  by  fine  lines,  and  to  have  the  centre  perpendicu- 
ar  or  at  right  angles  with  the  top.  The  plumb  line  should 
be  a  fine  smooth  silk  thread  or  hair.  At  z,  a  hole  should  be 
bored  of  a  suitable  size  to  set  it  on  the  head  of  a  compass 
staff.  Such  an  instrument,  if  correctly  made,  will  answer  all 
the  purposes  before  mentioned.! 

Before  directions  are  given  for  levelling,  the  difference 
between  the  apparent,  and  the  true  level,  will  be  explained. 
The  former  is  a  tangent,  or  a  straight  line,  drawn  and  con- 

*  An  angle  of  elevation  rises  above  a  horizontal  line ;  a  depression 
falls  below  it. 
t  This  instrument  may  be  improved  by  fixing  sights  on  the  top. 


APPENDIX.  133 

tinued  from  any  point  on  the  globe,  the  surface  continually 
departing  from  it.  The  latter  is  the  curvature  of  the  earth, 
or  a  line  parallel  with  it,  like  two  concentric  circles,  each 
part  of  the  true  level,  whatever  may  be  its  length,  is  equidis- 
tant from  the  centre  of  the  earth.  The  straight  line  m  n,  in 
the  following  figure,  represents  the  apparent,  and  the  curved 
line  a  z,  the  true  level. 


n 


Let  the  above  described  instrument  be  set  on  any  part' of 
the  ocean,  and  be  levelled  by  the  plummet,  the  top  being  even 
with  the  surface  of  the  water,  and  let  a  line  with  the  top  be 
continued;  as  the  plummet  hangs  directly  towards  the  centre 
of  the  earth,  it  is  evident  that  this  line  is  a  tangent,  and  at 
the  end  of  one  mile  it  will  be  8  inches,  at  the  end  of  10  miles 
66  feet  4  inches,  and  at  20  miles,  266  feet  above  the  surface 
of  the  water.  m 

In  levelling  between  two  points  at  a  considerable  distance 
apart,  where  the  instrument  must  be  often  set,  as  the  plum- 
met, like  the  spokes  in  a  wheel,  each  time  hangs  directly 
towards  the  centre  of  the  earth,  it  will  keep  the  top  of  the 
instrument  on  the  true  level,  provided  it  is  set  on  the  centre 
of  each  stationary  distance.  But  when  the  level  is  taken 
from  the  first  to  the  second  station,  and  from  the  second  to 
the  third,  and  so  on  in  succession  to  the  end,  each  level  will 
be  a  tangent ;  of  course,  the  apparent  level  will  be  taken. 

The  surveyor  should  also  be  furnished  with  two  observa- 
tion staves,  ten  feet,  or  more,  in  length,  divided  into  feet  and 
inches.  These  staves  should  be  committed  to  the  care '  of 
Uvo  skilful  men,  who  will  keep  them  perpendicular  at  the 
stations,  and  who  will  be  correct  in  their  assistance  in  taking 
the  observations.  Suppose  the  first  stationary  distance,  on 
which  a  level  is  to  be  taken,  is  20  rods.  The  staves  must 
be  erected  at  each  terminating  point,  and  the  surveyor  must 
take  his  station  equidistant  from  each.  A  target  must  be 
raised  on  each  staff  as  the  surveyor  may  direct. 

If  the  level  strikes  the  back  staff  7  feet,  and  the  forward 
staff  2  feet,  above  the  surface,  it  is  apparent  that  the  rise  be- 
tween the  stations  is  5  feet ;  but  the  substraction  need  not  be 
made,  each  observation  should  be  entered  in  its  respective  col- 
umn, under  the  head  of  fore  heights  and  back  heights,  or  fore 
sights  and  back  sights,  as  the  surveyor  may  choose  to  term 
them. 

When  the  first  observation  is  completed,  the  back  staff 
should  be  carried  forward  to  a  convenient  place,  and  the 
12* 


134  APPENDIX, 

second  observation  taken  as  the  first.  In  like  manner  the 
rest  of  the  observations  must  be  taken  and  entered  in  their 
respective  columns. 

If  the  sum  of  the  back  sights  shall  exceed  the  fore  sights, 
the  terminating  point  is  higher  than  the  place  of  beginning ; 
but  if  the  sum  of  the  fore  sights  shall  exceed  the  back  sights, 
then  the  terminating  point  is  lower  than  the  point  of  begin- 
ning, as  will  appear  by  the  following  examples. 

FIRST  EXAMPLE. 

Pore  sights.  Back  sights. 

Feet.  Inches.  Feet.  Inches, 

1st  Observation     7  00  0  00 

2d           "             8  00  2  00 

3d           "              8  00  1  00 

4th          "              7  00  2  00 

5th          "              7  00  2  00 

6th          "              1  00  7  00 

7th          M              I  00  8  00 

8th          "              1   00  8  00 

9th          "              1  00  8  00 

10th        "              0  00  8  00 

41  00  46  00 

41  00 

Difference  5  00 

The  terminating  point  is  5  feet  higher  than  the  point  of 
beginning. 

SECOND  EXAMPLE. 

Fore  sights.  Back  sights. 

Feet.  Inches.  Feet.  Inches. 

1st  Observation    7  00  0  00 

2d           "              8  00  2  00 

3d           "              8  00  1   00 

4th         "             7  00  2  00 

5th         "             7  00  2  00 

6th         -              1  00  7  00 

7th         "        .      1  00  8  00 

8th         "              1  00  8  00 

9th         "              1  00  8  00 


41  00  38  00 

38  00 


Difference     3  00 


APPENDIX.  135 

The  terminating  point  is  3  feet  lower  than  the  point  of 
beginning. 

When  the  sums  of  the  two  columns  are  equal,  the  ex- 
treme points  are  on  the  same  level.  It  will  not  be  necessa- 
ry to  enter  the  stationary  distances  in  the  field  notes,  unless 
the  whole  distance  between  the  two  extreme  points,  or  a  pro- 
file of  the  surface,  is  wanted. 

On  a  distance  of  80  rods,  the  difference  between  the  ap- 
parent and  true  level,  is  half  an  inch ;  at  half  a  mile,  two 
inches. 

In  levelling  to  ascertain  how  high  a  dam  across  a  stream 
may  be  raised  without  flowing  the  meadows,  or  impeding 
the  wheel  of  a  mill  above,  great  caution  should  be  observed, 
for  if  a  dam  is  raised  to  a  level  with  a  point  80  or  100  rods 
above,  to  which  it  may  be  supposed  that  water  may  flow 
without  damage,  it  will  rise  higher  at  that  point  than  any 
one  would  suppose,  who  has  not  investigated  the  subject. 
The  rise  of  water  at  the  head  -of  a  pond,  will  depend  in  a 
great  measure  on  the  width  of  it,  and  on  the  size  and  force 
of  the  stream. 

In  locating  roads,  sometimes  it  is  necessary  to  ascertain 
the  difference  between  the  elevation  of  the  hills  on  two 
routes,  both  proceeding  from  one  and  terminating  at  the 
same  point.  Though  the  difference,  of  itself,  between  the 
rise  and  fall  on  two  routes,  may  not  in  all  cases  be  a  correct 
rule  by  which  to  give  preference,  yet  this  evidence,  with  a 
comparison  between  the  steepness  of  the  hills  on  two  routes, 
is  sufficient. 

To  perform  this  service  by  the  slow  process  of  levelling 
for  the  conveyance  and  rise  of  water,  would  be  attended 
with  an  expense  which  the  case  would  not  justify ;  therefore, 
a  more  expeditious  method  will  be  pointed  out.  At  conve- 
nient distances,  take  all  the  angles  of  elevation  and  of  de- 
pression, with  the  instrument  before  described,  measuring 
the  distance  between  each  station.  These  angles  will  be 
taken  more  correctly  by  back  sights,  as  the  surveyor  can 
better  select  proper  places  for  taking  them  than  an  inexpe- 
rienced assistant.  The  courses  or  bearings  of  the  several 
stationary  distances,  may  or  may  not  be  taken  with  a  com- 
pass. 

The  elevation  of  the  hills  may  be  ascertained  as  correctly 
without  the  courses  as  with  them.  If  the  courses  are  taken, 
it  will  require  more  time  and  expense.  Having  measured 
all  the  stationary  distances,  and  taken  all  the  angles  of  ele- 
vation and  depression  on  a  route,  arrange  them,  as  in  the 
following  table.  The  first  column  contains  the  number  of 


136 


APPENDIX. 


stations;  the  second,  the  distances  in  rods;  the  third,  the 
degrees  of  elevation  or  depression,  with  the  letter  E.  or  D. 
against  them.  The  column  H.  D.  contains  the  horizontal 
distance  made  on  each  line.  The  horizontal  distance,  with 
the  elevation  or  depression  against  it,  is  the  same  as  the 
latitude  and  departure  on  a  course  taken  by  the  compass. 
The  column  P.  H.  contains  the  perpendicular  height  at  the 
end  of  each  line  above  the  horizontal  line.  This  column,  in 
this  case,  is  formed  by  adding  the  elevations,  and  bysubstract- 
ing  the  depressions. 


it 

o 

Dist. 

rods. 

o 

H.D. 

E. 

D. 

P.H. 

1 

50. 

4 

E. 

49.88 

3.49 

3.49 

2 

40. 

5 

E. 

39.85 

3.49 

6.98 

3 

30. 

3 

E. 

29.96 

1.57 

8.55 

4 

20. 

2 

D. 

19.99 

.70 

7.85 

5 

40. 

4 

D. 

39.90 

2.79 

5.06 

6 

50. 

3 

D. 

49.93 

2.62 

2.44 

7 

45. 

1 

~c^ 

44.99 

.79 

3.23 

8 

40. 

4 

E. 

39.90 

2.79 

6.02 

9 

50. 

3 

E. 

49.93 

2.62 

8.64 

10 

40. 

1 

E. 

39.99 

.87 

9.51 

15.62 

6.11 

By  this  calculation  it  appears  that  the  sum  of  the  eleva- 
tions amount  to  15.62  rods,  or  to  257  feet  8f-  inches,  and  the 
depressions  amount  to  6.11  rods,  or  to  100  feet  9 f  inches, 
which  may  be  thus  expressed,  257  feet  8f  inches  rise,  and 
100  feet  9f  inches  fall.  It  also  appears  that  the  hill  at  the 
terminating  point  is  24  links,  or  15  feet  10  inches,  higher  than 
the  top  of  the  first  hill. 

By  this  method  of  taking  elevations,  they  are  the  appa- 
rent level,  but  this  will  answer  the  purpose  for  locating 
roads. 


APPENDIX.  137 


DIRECTIONS  TO  MAKE  A  PROFILE  OF  THE  ABOVE  SURVEY. 

Lay  the  plan  on  a  scale  of  ten  rods  to  an  inch.  Draw  a 
straight  line  about  3£  feet  in  length  for  a'  horizontal  line. 
On  this  line  lay  down,  the  several  horizontal  distances  as 
they  stand  in  the  table.  At  the  end  of  each  of  these  dis- 
tances lay  down  the  perpendicular  height  which  stands 
against  it,  at  right  angles  with  the  horizontal  line.  From 
one  of  these  points  to  another,  draw  a  line  from  the  begin- 
ning to  the  end,  which  will  represent  the  surface  of  the 
ground. 

Profiles  of  roads,  or  of  certain  hills  on  roads,  are  good 
evidence  to  carry  into  courts,  in  disputed  cases  of  this  kind. 
When  such  testimony  is  exhibited,  the  elevations  of  hills 
should  be  given  in  feet  and  inches,  Also,  the  rise  and  fall 
should  be  given  in  this  measure. 


MISCELLANIES. 

TO  REDUCE  CHAINS  AND  LINKS  TO  FEET  AND  INCHES. 
RULE. 

Multiply  the  chains  and  links,  or  any  number  of  links 
less  than  a  chain,  by  66,  the  number  of  feet  in  a  chain,  and 
from  the  product  point  off  two  figures  at  the  right,  for  deci- 
mals. The  figures  at  the  left  will  be  feet.  Multiply  the  de- 
cimals by  12,  the  number  of  inches  in  a  foot,  and  point  off 
two  figures  at  the  right.  Those  at  the  left  will  be  inches. 
Multiply  the  last  decimals  by  4,  and  point  off  two  figures  at 
the  right,  and  that  at  the  left  will  be  quarters  of  an  inch. 

EXAMPLE. 

In  2  chains  22  links,  how  many  feet  and  inches  1 
ch.   1. 
2.22 
66 

1332 
1332 


138  APPENDIX. 

104 
52 


6.24 
4 

.96  Ans.  146  ft.  6i  in.  nearly. 

1O  ASCERTAIN  THE  NUMBER  OF  INCHES  IN  A  LINK. 

As  it  will  not  increase  66  by  multiplying-  it  by  1,  multiply 
66  by  12,  and  the  product  will  be  7.92  inches. 

TO    REDUCE  INCHES  TO  THE  DECIMAL  OF  A  FOOT. 
RULE. 

Annex  two  ciphers  to  the  inches  and  divide  that  sum  by 
12,  and  the  quotient  will  be  the  decimal  required. 

EXAMPLE. 

What  part  of  a  foot  is  9  inches  ? 

12)900(.75 

84 

60 

60  Ans.  75  or  75-100. 

TO  REDUCE  FEET  AND  INCHES  TO  CHAINS  AND  LINKS. 
RULE. 

Reduce  the  inches  to  the  decimal  of  a  foot,  and  annex  that 
to  the  feet ;  or  if  there  are  no  inches,  annex  two  ciphers  to 
the  feet,  and  divide  that  sum  by  66,  and  the  quotient  will  be 
chains  and  links. 

EXAMPLE. 

In  440  feet  3  inches,  how  many  chains  and  links  ? 

66)440.25(6.67 
396 

442   . 
396 


APPENDIX.  130 

465 
462 

3  Ans.  6  ch.  67  links. 

When  a  piece  of  land  is  calculated  by  chains  and  links, 
and  the  contents  stand  in  acres  and  decimal  parts  of  an  acre, 
it  may  be  multiplied  by  the  price  of  an  acre,  and  the  product 
will  be  the  amount. 

EXAMPLE. 

A  piece  of  land  16  chains  and  75  links  in  length,  and  12 
chains  and  25  links  in  breadth,  is  sold  for  $25.25  per  acre, 
what  is  the  price  of  it? 

Length  .  16.75 

Breadth       -         -         -         12.25 


8375 
3350 
3350 
1675 

Acres  and  decimal  parts,         20.51875 

25.25 


10259375 
4103750 

10259375 

4103750 


Answer,         $518.09.84375,  or  $518.10. 

What  is  the  length  of  a  side  of  a  square  which  contains 
6040  acres? 

6040 
4 

24160 

40 
Logarithm  of  966400  £5.985 157 

2.992578.  Answer,  983.06  rods. 

What  is  the  length  of  a  side  of  a  square  which  contains 
4  acres,  or  640  rods  ? 


HO  APPENDIX. 

Logarithms  of  640  £2. 806 180 

1.403090.     Answer,  25.3  rods. 

A  four  sided  figure,  described  by  the  following  courses 
and  distances,  is  divided,  into  two  triangles  to  find  arithme- 
tically the  contents  of  each,  and  the  amount  of  both,  viz. 
A,  B.  N.  10°  E.  55  rods,  B,  C.  S.  85°  E.  65  rods,  C,  D.  S.  8° 
W.  60  rods,  D,  A.  N.  80°  35'  W.  66.85  rods.  The  supple- 
ment of  the  angle  contained  between  the  two  first  sides  is 
85°,  what  is  the  area  of  the  triangle  ? 

Sine  of  85°  -.       9.998344 

A,  B.  55  rods  1.740363 

B,  C.  65  do.  -         1.812913 


Cancel  the  first  figure  1,3.551620— Double  area  3561 

160)1780.5(11 
160 

180 
160 

A.   a   R. 

Answer,    11       0    20£  20.5 

The  angle  contained  between  the  two  last  sides  is  88°  35', 
what  is  area  ? 

Sine  of  88°  35'         -         9.999867 

C,  D.  60  rods  1.778151 

D,  A.  66.85  rods       -         1.825101 


Cancel  the  first  figure  1,3.603119— Double  area  4010 

.160)2005(12 
160 

A.  a  R  405 

Answer                    12    2    05  320 
First  triangle           1 1    0    20£ 

85 


Whole  contents        23    2    25^ 


Perhaps  the  above  is  as  short  and  as  certain  a  method  to 
calculate  the  contents  of  an  oblique  angled,  four  sided  figure, 
as  can  be  taken.* 

*  Any  polygon  may  be  reduced  to  triangles,  and  the  contents  cal- 
culated by  the  same  method. 


APPENDIX.  141 

The  method  of  calculating  areas  of  such  figures  by  multi- 
plying together  half  the  sum  of  the  two  opposite  sides,  is 
incorrect,  or  the  only  certainty  there  is  in  it,  is  that  of 
making,  in  a  greater  or  less  degree,  an  excess  of  quantity. 
In  cities,  it  is  the  practice  to  measure  lots  by  feet  and 
inches. 

To  calculate  the  areas  of  such  lots,  reduce  the  inches  to  the 
decimal  of  a  foot,  annex  such  decimals  to  the  feet  to  which 
they  belong,  and  calculate,  as  by  other  measure,  which  will 
give  the  areas  in  square  feet. 

When  it  is  required  to  give  the  areas  of  such  lots  in  square 
rods,  and  the  contents  stand  in  square  feet,  divide  the  feet 
by  272.25,  the  number  of  square  feet  in  a  rod,  and  the  quo- 
tient will  be  the  answer;  or  the  feet  and  inches  given  in  the 
distances,  may  be  reduced  to  chains  and  links,  or  to  rods  and 
decimal  parts  of  a  rod,  and  the  calculations  made  as  in  other 
cases.  In  measuring  city  lots,  as  step-stones  and  other  ob- 
structions may  be  in  the  way,  extend  a  rope  across  the  front. 
Let  it  be  level,  drawn  tight,  and  made  fast  at  each  end.  Mea- 
sure on  the  rope;  also,  measure  the  other  sides  with  equal 
accuracy,  if  necessary. 

In  the  two  first  editions  of  this  work,  a  rule  was  inserted  to 
prove  the  correctness  of  the  courses  in  a  survey,  but  it  was 
afterwards  discovered  by  Mr.  Flint,  and  by  others,  that  the  rule 
will  prove  courses  to  be  correctly  taken  when  they  are  incor- 
rect. 

The  same  rule  has  recently  made  its  appearance  in  the 
American  Journal  of  Science  and  Arts,  and  it  may  take  a 
second  tour  among  surveyors,  under  the  character  of  an  un- 
erring rule. 

FOR}*  O¥  A   FIELD  BOOK. 

Beginning  at  a  mere-stone  at  the  south-west  corner. 

Rods.  Links. 

1.  N.  25°  00'  E.  40  00  to  a  pine  tree. 

2.  N.  10  00  E.  30  00  to  a  hemlock  tree. 

3.  N.  75  00  E.  60  00  to  a  spruce  tree. 

4.  S.  10  00  W.  36  00  to  a  beech  tree. 

5.  S.  5  00  W.  40  00  to  a  maple  tree, 

6.  S.  85  05  W.  70  12  to  the  place  of  Deginning. 

On  account  of  the  diurnal  motion  of  the  magnetic  needle, 
in  the  warm  season  of  the  year,  the  courses  in  all  surveys, 
if  practicable,  should  be  taken  before  9  o'clock  in  the  morn 
ing, 

13 


142  APPENDIX. 

Let  this  matter  be  investigated.  A  survey  is  commenced 
at  seven  o'clock  in  the  morning,  but  is  not  completed  until 
three  o'clock  in  the  afternoon.  The  course  of  the  first  line 
is  N.  5°  E.,  and  the  distance  is  70  rods.  '  The  departure  on 
this  course  and  distance  is  6.10  rods. 

When  the  survey  is  completed,  the  bearing  of  this  line  is 
again  taken,  and  the  course  is  N.  5Q  10'  E.  The  departure 
is  now  6.30  rods,  five  links  more  than  it  was  in  the  morning. 
,  Every  compass  which  is  in  such  order  as  it  ought  to  be, 
will  generally  find  in  the  summer,  from  morning  to  one 
o'clock,  as  great  a  change  as  this,  often  greater,  but  seldom 
less. 

The  writer  knows  not  who  invented  the  following  rules  for 
finding  contained  angles,  but  they  have  been  extensively 
adopted  into  practice. 


When  the  first  letters  are  alike,  and  the  last 
unlike,  add  the  courses. 

When  the  first  letters  are  alike,  and  the  last 
also,  substract  the  less  course  from  the  greater. 


N.  62°  E. 

N.  44°   W. 

S.    72°  E. 

S.    25°  E. 

N    64°  F     ?      When  the  first  letters  are  unlike  and  the  last 

a     oro  XT-     >  alike,  add  the  courses,  and  substract  their  sum 

K    $from  180°. 

N    57°  W  )      When  the  first  and  the  last  letters  are  unlike, 
Q     9*0  -p     ?  substract  the  less  course  from  the  greater,  and 

~-    >  the  remainder  from  180°. 

To  find  the  quantity  of  an  angle,  reverse  the  preceding 
course,  then  both  courses  will  run  from  the  same  point. 
These  rules  are  applied  only  when  the  first  course  is  re- 
versed. 

EXAMPLE. 

Two  courses  are  given,  viz.  S.  62°  W.,  and  N.  44°  W.  to 
find  their  contained  angle.  Suppose  yourself  standing  at  the 
point  where  these  courses  meet.  Reverse  the  letters  of  the  first 
course,  and  they  will  stand  thus : 

N!  44-  W.  I      The  first  rula 

The  following  figures  were  prepared  for  the  sixth  edition 
of  this  treatise,  by  Mr.  Barnard.*  There  is  nothing  in  the 
rules  to  which  they  are  applied,  different  in  principle  from  the 
preceding  ones,  but  they  do  not  require  the  first  course  to  be 
reversed. 

*  Such  notes  on  the  text  as  are  signed  ED.,  were  made  by  Mr,  Barnard. 


APPENDIX. 


143 


I.  If  the  first  letters  are  alike,  and  the  last  also,  add  the 
less  course  to  the  supplement  of  the  greater. 

II.  If  the  first  letters  are  alike,  and  the  last  unlike,  sub- 
stract  the  sum  of  the  courses  from  180°. 

III.  If  the  first  letters  are  unlike,  and  the  last  alike,  add  the 
courses. 

IV.  If  the  first  letters  are  unlike,  and  the  last  also,  sub- 
stract  the  less  course  from  the  greater. 

"  A  set  of  figures  like  the  following,  well  fixed  in  the  mind, 
will  be  a  great  assistance  to  the  learner." 


RULE  1st. 

N.  20°  E. 
N.  70  E. 


RULE  2d. 

N.  500  E> 
N.  40  W. 


JS 


RULE  3rd. 
N.  25°  E. 
S.  60  E. 


RULE  4th. 

N.  82°  E. 
S.  25  W. 


"  It  will  be  seen  that  the  required  angle,  in  each  case,  is 
A,B,C." 


144  APPENDIX. 


CONVERGING  OF  MERIDIANS. 

Two  meridians  cannot  be  run  by  the  compass  parallel  to 
each  other,  for  they  will  diverge  towards  the  equator,  and 
converge  towards  the  pole. 

The  length  of  a  degree  of  longitude  in  any  parallel  of 
latitude,  is  to  the  length  of  a  degree  upon  the  equator,  as  the 
co-sine  of  that  latitude  is  to  radius. 

The  following  proportion  will  give  the  length  of  a  degree 
of  longitude  in  any  parallel  of  latitude. 

As  radius  is  to  the  length  of  a  degree  on  the  equator,  so 
is  the  co-sine  of  the  latitude,  to  the  length  of  a  degree  on 
that  latitude.  This  rule  may  be  applied  either  to  geographi- 
cal or  to  statute  miles. 

A  degree  on  the  equator  of  geographical  measure,  is  60 
miles ;  that  of  statute  measure  has  been  estimated  at  69^ 
miles,  but  this  estimate  is  too  great. 

The  earth  is  considered  a  sphere,  7930  statute  miles  in 
diameter.  By  the  rules  contained  in  this  book  for  calcula- 
ting the  circumference  of  a  circle,  when  the  diameter  is 
given,  the  circumference  of  the  earth  will  be  found  24912.8 
miles.  This  number  divided  by  360,  gives  a  quotient  of  69.2, 
the  length  of  a  degree  upon  the  equator. 

FIRST    EXAMPLE. 

What  is  the  length  of  a  degree  of  longitude  in  geographi- 
cal miles  in  latitude  42  ? 

As  radius  10.000000 

:  is  to  60  miles  1.778151 

:  :  so  is  co-sine  of  latitude  42o  9.871073 


11.649224 
10.000000 

:  Answer,  44.59  miles.  L649224 

SECOND  EXAMPLE. 

What  is  the  length  of  a  degree  of  longitude  in  statute 
miles  in  latitude  42°  ? 

As  radius  ....         10.000000 

:  is  to  69.  2  miles       -  1.840106 

::  so  is  co-sine  of  lat.  42°    -        -          9.871073 


APPENDIX,  145 

11.711179 

10.000000 

Answer,  51.42  miles.  1.711179 

DIVERGENCE  OF  THE  COMPASS  FROM  PARAL- 
LELS OF  LATITUDE. 

When  a  meridian  crosses  a  parallel  of  latitude,  the  angles 
on  the  side  opposite  to  the  equator  are  equal,  and  each  con- 
tains less  than  90° ;  of  course,  those  on  the  other  side  are  equal, 
and  each  contains  more  than  90°.  This  is  demonstrated  by  the 
meridians  and  parallels  on  a  globe.  The  difference  between 
the  first  and  second  angles,  depends  on  their  distance  from 
the  equator.  In  70°  of  latitude,  the  two  first  are  less,  and 
the  two  last  are  greater  than  they  are  in  10°  of  latitude. 

When  the  compass  is  set  on  a  parallel  of  latitude,  at  right 
angles  with  a  meridian,  it  is  apparent  that  each  angle  con- 
tains 90°;  of  course  the  compass  will  not  run  on  that  paral- 
lel, but  will  diverge  from  it,  and  by  continual  running  will 
arrive  at  and  run  on  the  equator. 

In  70°  of  latitude,  the  compass  tends  towards  the  equator 
faster  than  it  does  in  10°,  hence  it  is  evident  that  an  east  or 
west  line,  run  by  the  compass,  is  not  straight,  but  is  curved. 

On  an  extensive  plain,  let  a  line  be  run  east  or  west  to  the 
distance  of  some  miles ;  then  from  the  terminating  point, 
back  on  the  opposite  course,  the  compass  will  not  return  on 
its  first  track  to  the  place  of  beginning,  but  will  fall  towards 
the  equator. 

The  divergence  of  the  compass  from  parallels  of  latitude, 
cannot  materially  affect  common  land  surveying ;  but  lines 
10,  20,  or  30  miles  in  length,  when  designed  to  be  run  on 
particular  parallels,  will  be  affected  by  it,  unless  calculations 
are  made  to  keep  the  compass  on  such  parallels. 


QUESTIONS. 

1.  At  a  certain  point,  I  took  the  elevation  of  a  tower,  3° 
15',  then  measured  towards  the  tower  on  an  angle  of  depres- 
sion 7°  333  feet,  to  a  level  with  the  base  of  the  tower ;  when  I 
took  the  elevation  again,  8°.  Required,  the  height  of  the 
tower,  and  the  distance  from  the  second  place  of  observation 
to  the  base ;  also,  how  much  higher  the  land  was  at  the  place 
of  the  first  observation,  than  at  the  second. 
13* 


146  APPENDIX, 

Answer.     Height  99.6  feet. 

Distance  required          -       708.6  feet. 
Difference  in  height  of  land  40.58  feet. 

2.  Two  persons  made   observations  on  the  altitude  of  a 
meteor,  both  being  on  the  same  side  of  it,  and  in  a  vertical 
plane  passing  through  it.     The  distance  between  their  sta- 
tions was  200  rods,  and  at  one,  the  angle  of  elevation  was  36° 
25',  at  the  other  32°  50',  and  at  the  last  the  disk  of  the  meteor 
subtended  an  angle  of  5'.     Required,  the  distance  from  the 
last  place  of  observation,  also  the  height  and  diameter  of  it. 

M.  a.  R. 

Answer.     The  distance  5    3    60 
Height,  3    0    70 

Diameter,     45  feet  5£-  inches. 

3.  From  the  top  of  a  steeple  165  feet  high,  the  angle  of 
depression  of  the  nearest  bank  of  a  river  is  11°  15',  that  of 
the   opposite  bank   is   6°    15'.     Required,  the  width  of  the 
river. 

Answer,  41.13  rods. 

4.  What  length  of  cart  tire  will  it  take  to  band  a  wheel  5 
feet  in  diameter  ? 

Answer,  15  feet,  8J  inches. 

5.  A  gentleman  laid  out  a  garden  in  a  circle,  containing 
one  acre,   one  quarter,  and  one  rod,   with  a  gravelled  walk 
on  the  outer  side  of  it  within  the  circle,  which  took  up  twelve 
rods   of  ground.     What  is   the  diameter   of  the  circle,  and 
what  is  the  width  of  the  walk  ? 

Answer.     The  diameter  16  rods — width  of  the  walk  4  feet. 

6.  Neptune  laid  out  1,000  square  miles  of  the  surface  of 
the  sea  in  a  circle,  and  sold  to  ^Eolus  all  that  part  of  it 
which  lies  without  a  concentric  circle  of  one  third  of  the 
diameter.     What  is  the  diameter,  and  how  much  was  sold  ? 

Answer.     The  diameter  35.68  miles. 
The  quantity  sold  888.92  square  miles. 

7.  A  farmer  laid  out  an  elliptical  orchard,  the  longest  di- 
ameter of  which  was  30  rods,  and  the  shortest  was  20  rods, 
and  enclosed  the  same  with  a  wall  two  feet  thick  within  the 
figure.     What  is  the  quantity  within  the  wall,  and  how  much 
is  covered  by  it  ? 


APPENDIX.  147 

A.  a  R. 

Answer.  Within  the  wall     2    3    22 
Covered  by  the  wall          9.3 

8.  From  a  point  in  an  equilateral  triangle,  I  measured  the 
distances  to  each  corner,  and  found  them  20.28,  and  31  rods. 
Required  the  area  and  the  length  of  the  sides.* 

A.  a.  R. 

Answer.  The  area  5     1     36£ 

Length  of  each  side  45  rods. 

9.  Required  the  dimensions  of  a  parallelogram  containing 
one  acre  and  a  half,  bounded  by  64  rods  of  fence. 

Answer,  12  by  20  rods. 

10.  The  area  of  a  parallelogram  is  five  acres,  one  quarter, 
and  thirty  five  rods,  and  the  diagonal  is  43  rods.     Required 
the  length  of  the  sides. 

Answer,  35  by  25  rods. 

11.  Required  the  dimensions  of  a  parallelogram  contain- 
ing   twenty-six   acres,    one   quarter,   and   twenty-four   rods, 
when  the  length  exceeds  the  breadth  by  fifty-two  rods. 

Answer,  44  by  96  rods. 

12.  Required  the  dimensions  of  a  parallelogram  contain- 
ing  250    acres,  when    the    sides  are  in  the  proportion   of 
7  to  3. 

Answer,  305 %  by  130.93  rods. 

13.  John  and  Jonathan  divided  a  lot  of  land  equally  as  to 
value,  which  contained  600  acres,  and  which  was  appraised 
at  $2  per  acre.     John's  division  was  valued  at  50  cents  per 
acre  more  than   Jonathan's.     What  were  the  contents   and 
price  per  acre   of  each  division.     Answer.  John's   division 
contained  263  acres  and   12  rods,  and  the  price  per  acre  was 
$2.28  1-10  nearly. 

Jonathan's  division  contained  336  acres,  3  roods,  and  28 
rods,  and  the  price  per  acre  was  $1.78  1-10  nearly. 

14.  The  state  of  Connecticut  contains  a  little  more  than 
4,828  square  miles,  or  3,090,000  acres,  including  rivers,  har- 
bours, creeks,  roads,  &c.     If  this  quantity  is  laid  in  a  square, 
what  will  be  the  length  of  a  side  ? 

*  This  may  be  solved  geometrically. 


148  APPENDIX. 

M.  a.  R. 

Answer,   69    1    75.11, 

One  word  of  advice  to  the  young-  surveyor,  who  is  com- 
ing forward  to  be  useful  in  his  occupation,  will  close  the  ap- 
pendix. 

In  the  choice  of  assistants  to  perform  practical  operations, 
never  call  to  your  aid  Sir  Richard  Rum.  He  frequently 
changes  his  name  to  brandy,  gin,  whiskey,  $c.  He  is  trea- 
cherous, and  he  causes  the  head  to  whirl,  the  body  to  reel, 
and  the  foot  to  stumble. 

By  his  might,  the  strong  man  has  fallen,  and  the  promis- 
ing youth  has  been  brought  to  an  untimely  grave. 

If  you  employ  Sir  Richard,  your  columns  of  latitude  may 
differ  too  much  for  correct  work,  and  your  columns  of  de- 
parture may  be  still  worse.  He  never  can  render  you  the 
least  service  in  establishing  your  reputation  as  an  accurate 
surveyor,  but  there  is  danger  that  he  may  do  much  to  destroy  it. 

NOTE. — Such  theory  as  is  more  curious  than  useful,  how- 
ever correct  it  may  be,  has  been  excluded  from  the  appendix. 
The  plainest  methods  have  been  selected.  On  some  points, 
the  Author  has  been  more  minute,  on  account  of  the  fact 
that  many  copies  of  this  book  are  bought  by  men  who  do 
not  expect  to  be  surveyors,  and  who  do  not  place  themselves 
under  instructors. 

If  some  repetition  is  to  be  found  in  this  work,  the  learner 
will  find  less  fault  with  it  than  the  critic. 

Hebron,  (Conn.)  June,  1835. 


LOGARITHMS. 


THE  learner,  who,  for  the  first  time,  becomes  acquainted  with  the 
wonderful  properties  of  Logarithms,  may  be  not  a  little  surprised  to 
find  himself  introduced  to  a  system  of  numbers,  so  new  in  their  nature, 
and  which,  surpassing  all  his  former  knowledge  of  figures,  afford  so 
many  facilities  for  shortening  the  labour  and  lessening  the  difficulty  of 
arithmetical  calculations. 

He  will  admire  to  find,  that  by  help  of  these,  the  labour  of  hours,  and 
in  some  calculations,  even  the  labour  of  days,  may  be  reduced  to  as  ma- 
ny minutes  !  The  invention  of  Logarithms  was  justly  regarded  as  "  a 
favour  from  heaven;"  because,  in  many  departments  of  science,  essen- 
tial to  the  happiness  of  man,  they  have  saved  him  ages  of  toil. 

Although  it  does  not  come  appropriately  into  the  design  of  a  work 
like  this,  to  enter  minutely  into  the  history  of  their  invention,  nor  the  yet 
more  difficult  process  by  which  they  were  originally  constructed,  yet  a 
familiar  explanation  of  their  properties  and  uses,  adapted  to  the  appre- 
hension and  wants  of  the  practical  surveyor,  is  necessary,  in  order  to  his 
making  a  proper  application  of  their  great  advantages  in  practice. 

Logarithms,  then,  we  may  first  observe,  never  stand  for  the  numbers 
themselves,  of  which  they  are  composed,  but  invariably  for  other  num- 
bers, of  \vhich  they  are  only  the  representative  exponents,  or  indices. 
Their  great  utility  in  arithmetical  operations,  consists,  chiefly,  in  this, 
— that  addition  takes  the  place  of  multiplication,  and  substraction  that 
of  division.  That  is,  to  multiply  numbers,  we  have  only  to  add  their  lo- 
garithms ;  to  divide,  we  have  only  to  substract  the  logarithm  of  the  divi- 
sor from  that  of  the  dividend  ;  to  raise  a  number  to  any  power,  we  multi- 
ply its  logarithm  by  the  exponent  of  that  power ;  and  to  extract  the  root  of 
any  number,  we  merely  divide  its  logarithm  by  the  number  expressing  the 
root  to  be  found. 

The  constant  number  upon  which  the  tables  in  common  use  are  con- 
structed, and  which  is  called  the  base  of  the  tables,  is  10;  and  every 
conceivable  number,  large  or  small,  integral,  mixed,  or  decimal,  is 
considered  as  some  ascertained  power  or  root  of  10. 
Indices.  Numbers.  Logarithms. 

101  the  first  power  of  ten  is  10,  whose  exponent  is          1. 

102  the  second  power  of  ten  is          100,  whose  exponent  is          2. 

103  the  third  power  often  is         1,000,  whose  exponent  is          3. 
10*  the  fourth  power  of  ten  is     10.000,  whose  exponent  is          4. 
105  the  fifth  power  of  ten  is        100,000,  whose  exponent  is          5. 
10s  the  sixth  power  of  ten  is  1,000,000,  whose  exponent  is          6. 

NOTE.  It  may  be  remarked,  that  the  first  power  of  any  number,  is  that  number 
once  repeated,  or  it  is  the  number  itself:  The  second  power  of  any  number  is 
the  product  of  that  number  multiplied  once  by  itself:  The  third  power  of  a  num- 
ber, is  the  product  of  the  number  multiplied  twice  by  itself;  the  fourth  power 
of  a  number,  is  the  product  multiplied  three  times  by  itself,  &c.  The  index  de- 
noting the  power,  is  called,  in  common  arithmetic,  the  exponent  of  that  power; 
and  is,  in  other  words,  the  logarithm  of  the  power. 

Logarithms,  then,  are  the  Exponents  of  a  series  of  powers  and  roots. 

In  the  above  series,  the  logarithms  indicate  how  many  ciphers  belong 
to  their  corresponding  numbers.  Thus,  the  logarithm  1  stands  for  10, 
or  1  and  one  cipher ;  the  logarithm  2  stands  for  100,  or  1  and  two  ci~ 


150  APPENDIX. 

phers ;  the  logarithm  3  for  1000,  or  1  and  three  ciphers,  &c.  Now,  if 
we  multiply  10,000  by  100,  the  product  will  be  1,000,000,  whose  loga- 
rithm is  6;  but  to  obtain  this,  we  need  only  add  the  logarithms  2  and  4, 
which  stand  opposite  the  numbers  to  be  multiplied.  On  the  contrary, 
if  we  divide  1,000,000  by  100,  the  quotient  will  be  10,000,  whose  loga- 
rithm is  4  :  but  to  obtain  this,  we  need  only  tosubstract  2,  the  logarithm 
of  the  divisor,  from  6,  the  logarithm  of  the  dividend. 

Again,  the  square  of  1000,  that  is,  the  product  of  1000  multiplied  by 
itself,  is  1,000,000,  whose  logarithm  is  6;  but  to  obtain  the  square  of 
1000,  we  need  only  double  its  logarithm  3.  On  the  other  hand,  the 
cube  root  of  1,000,000  is  100,  whose  logarithm  is  2 ;  but  this  is  obtained 
by  dividing  0,  the  logarithm  of  the  given  number,  by  3,  the  index  of 
the  root.  Hence  it  is  manifest,  that  the  protracted  labour  of  multiplying 
or  dividing  one  large  number  by  another,  the  tedious  evolution  of  roots, 
and  the  various  mistakes  incident  to  long  operations,  may  be  almost 
entirely  obviated  by  the  use  of  logarithms. 

As  the  logarithm  1  is  always  0,  and  that  of  10  is  but  1,  the  logarithms 
of  all  numbers  bdoiv  10,  will  be  decimals;  and  as  the  logarithms  in  the 
common  system  increase  regularly  by  1,  according  to  the  integral  pow- 
ers of  10,  it  follows  that  the  logarithms  of  all  numbers  between  10  and 
100,  will  be  more  than  1,  but  less  than  2 — that  is,  they  will  be  1  and  a 
decimal;  the  logarithms  of  all  numbers  between  100  and  1000,  will  be 
between  2  and  3— that  is,  they  will  be  2  and  a  decimal;  and  the 
logarithm  of  all  numbers  between  1000  and  10;000,  will  be  between  3 
and  4 — that  is,  3  and  a  decimal. 

A  logarithm  generally  consists  of  two  parts ;  a  whole  number,  and  a 
decimal.  This  whole  number,  or  integer,  is  called  the  characteristic,  or 
index,  of  the  logarithm,  and  is  always  one  less  than  the  number  of  inte- 
gral figures  in  the  natural  number,  whose  logarithm  is  sought.  As  the 
index  of  the.  logarithm  is  omitted  in  the  tables,  it  is  important  to  recol- 
lect the  principle,  or  rule,  by  which  it  is  to  be  supplied,  whenever  it  is 
wanted  in  calculation.  Thus,  the  logarithm  of  8  is  0.903090."  Here, 
the  number  (8)  consists  of  but  one  figure,  and  the  index  of  its  logarithm, 
being  one  less,  must  be  0.  Again,  the  logarithm  of  16  is  1.204120. 
Here,  the  given  number  (16)  consists  of  two  figures,  and  the  index  of 
its  logarithm,  being  one  less,  must  be  1.  Again,  the  logarithm  of  640  is 
2.806180.  Here,  the  given  number  (640)  consists  of  3  figures,  and  the 
index  of  its  logarithm,  being  one  less,  must  be  2,  &c.  The  rule  holds  uni- 
versally true,  that  the  index  of  a  logarithm  is  always  one  less  than  the 
number  of  integral  figures  in  the  natural  number,  whose  logarithm  is 
sought. 

The  same  rule  holds  in  mixed  numbers.  The  logarithm  of  6.40  is 
0.806180,  the  same  as  for  640,  (see  the  last  example,")  differing  only  in 
the  index.  Here,  the  integral  part  (6)  of  the  given  number,  consists  of 
but  one  figure,  and  the  index  of  its  logarithm,  being  one  less,  must  be  0. 
And,  generally,  having  obtained  the  logarithm  of  any  number,  large 
or  small,  we  have  only  to  change  the  index,  agreeably  to  the  above 
rule,  in  order  to  obtain  the  logarithm  of  every  other  number,  consist- 
ing of  the  same  significant  figures,  whether  they  be  integral,  fractional, 
or  mixed.  Thus : — 

The  logarithm  of  7596  is  3.880585 

759  6  2.880585 

75.96  1.880585 

7.596  0.880585 

.7596         —1.880585 

.07596        —2.880585 

,007596       —3.880585 


APPENDIX.  151 

When  the  natural  number  is  less  than  1,  the  index  of  its  logarithm 
becomes  less  than  0,  or  negative  ;  and  is  indicated  by  placing  the  sign, 
— ,  just  before,  or  above  it.  Suppose  it  were  required  to  affix  the  proper 
index  to  the  logarithm  of  .000007596.  Here,  the  number  of  cyphers 
on  the  left,  including  the  decimal  point,  is  6,  which  being  fitted  with  the 
negative  sign,  — ,  becomes  the  proper  index  of  the  logarithm.  And 
Universally,  The  negative  index  is  always  equal  to  the  number  of  ci* 
phcrs  on  the  left,  including  the  decimal  point. 

Before  any  one  can  avail  himself  of  the  great  advantages  of  loga- 
rithms, in  expediting  the  operations  of  Arithmetic  and  Trigonometry, 
he  must  become  so  familiar  with  the  tables,  that  he  can  readily  find  the 
logarithm  of  any  number;  and,  on  the  other  hand,  the  number  to 
which  any  logarithm  belongs. 


DIRECTIONS  FOR  TAKING  LOGARITHMS  AND  THEIR  NUMBERS  FROM  THE  TABLE. 

NOTE.  In  the  common  tables,  the  Indices  to  the  logarithms  of  the  first  100  num- 
bers are  inserted.  But  for  all  other  numbers,  the  decimal  part  only  of  the  lo- 
garithms is  given  :  while  the  index  is  left  to  be  supplied,  according  to  the  prin- 
ciples already  laid  down. 

PROBLEM  I. —  To  find  the  logarithm  of  a  number  between  1  and  100, 

RULR.  Look  for  the  proposed  number  on  the  left;  and  against  it,  in 
the  next  column,  will  be  the  logarithm  with  its  index. 

EXAMPLE.  The  logarithm  of  50  is  1.698970.  The  logarithm  of  89 
is  1.949390. 

PROBLEM  II.  To  find  the  logarithm  of  any  number  between  1  and 
1000:  or  of  any  number  consisting  of  not  'more  than  three  significant 
figures,  with,  ciphers  annexed. 

RULE.     Find  the  given  number  in  the  left  hand  column  of  the  table, 
next  column,  is  the  clecirr 
index,  as  already  taught. 

EXAMPLE.     The  logarithm  of  140  is  2,146128.     The  logarithm  of 


and  directly  opposite,  in  the  next  column,  is  the  decimal  part  of  its  lo- 
garithm, to  which  apply  the  i    ' 


781  is  2.892651 ;  of  358  is  2.553883  ;  of  974  is  2.988559. 

The  decimal  part  only  of  these  logarithms  are  found  in  the  table  ; 
the  index  2,  was  affixed  to  each,  because  the  given  numbers  consisted, 
each,  of  three  integral  figures.  If  there  had  been  ciphers  annexed  to 
thefsignincant  figures  of  the  given  numbers,  as  1400,  35800,  &c.,  their 
logarithms  would  have  been  precisely  the  same,  with  the  exception  of 
the  index  only  ;  and  consequently,  would  be  found  in  the  same  place  in 
the  table.  Thus : — 

The  log.  of  1400  is  3.146128.  The  log.  of  781000  is  5.892651. 

of  35800      4.553883.  of  9740000      6.988559. 

Here  the  decimal  part  of  the  logarithm  is  the  same  as  before  ;  while 
the  index  has  been  increased  as  many  units,  as  there  are  ciphers  annexed 
to  the  given  numbers.  This  rule  will  hold  good  in  all  similar  cases. 

PROBLEM  III.  To  find  the  logarithm  of  any  number  consisting  of 
four  figures,  either  with  or  without  ciphers  annexed. 

RULE.  Look  for  the  three  first  figures,  on  the  left  hand,  and  for  the 
fourth  figure,  at  the  top  of  one  of  the  columns ;  the  logarithm  will  be 


152  APPENDIX. 

found  opposite  the  three  first  figures,  and  in  the  column  which,  at  the 
head,  is  marked  with  the  fourth  figure. 

By  reference  to  the  table,  it  will  be  seen,  that  each  page  contains  ten 
columns  of  logarithms,  which  are  severally  numbered  from  0  to  9. 
The  first  column,  alone,  contains  six  figures;  while  every  other  column 
has  only  four  figures  :  but  it  is  to  be  always  remembered  that  the  two 
first  figures  of  the  left  hand  column,  are  common  to  each  of  the  other 
columns,  and  were  omitted  only  to  avoid  repetition.  These  two  initial 
figures,  therefore,  are  to  be  prefixed  to  each  of  the  other  four,  since 
every  logarithm,  in  our  table,  consists  of  six  figures,  besides  the  index. 
EXAMPLE.  The  log.  of  3657  is  3.563125.  The  log.  of  6704  is  3826334. 
of  5696  is  3.755570.  of  8512  is  3.930032. 

In  the  last  example,  as  it  will  frequently  happen,  the  two  initial 
figures  (93)  of  the  logarithm,  are  not  found,  in  the  same  line,  with  the 
given  number,  (851,)  but  in  the  next  below  it: — And,  universally, 
\vhenever  the  third  figure  of  the  logarithm  changes,  from  9  to  10,  the 
cipher  only  is  retained  in  the  column,  while  the  one  is  carried  down 
to  the  next  lower  initial,  on  the  left.  To  guard  against  a  mistake  here, 
points  have  been  substituted  in  place  of  ciphers;  and  wherever  these 
points  are  found,  the  ciphers  are  to  be  reinstated,  and  the  two  initials 
taken  from  the  line  below.  To  be  more  particular,  in  the  above  exam- 
ple ;  on  turning  to  page  14  of  the  logarithms,  and  against  851,  the 
learner  will  find  92  for  the  two  initial  figures,  which  he  must  prefix  to 
the  other  four  figures  in  Ihe  first  and  second  columns,  but  no  farther. 
There  he  must  stop,  and  taking  the  two  initial  figures  in  the  line  be- 
low, against  852,  carry  them  up  to  the  third  column,  where  ihe  dots 
commence,  and  prefix  the  same  to  each  of  the  remaining  columns:  and 
so  in  all  similar  cases. 

PROBLEM  IV.  To  find  the  logarithm  of  a  number  consisting  of 
five  or  six  figures. 

RULE.  Find  the  logarithm  of  ihe  first  four  figures  of  the  give'n  num- 
ber, as  taught  in  the  last  problem.  Take  the"  remain  ing  figures  and 
multiply  them  into  the  number  standing  opposite,  in  the  outside  column, 
headed  D;  from  the  right  of  the  product,  reject  as  many  figures  as  yon 
multiplied  by,  and  add  what  is  left  to  the  logarithm  previously  found. 
This  sum,  being  fitted  with  a  proper  index,  will  be  the  logarithm 
required. 

EXAMPLE.     Required  the  logarithm  of  45263.     Thus — 

The  logarithm  of  45260  is  4.655715 

The  difference  D  is  96,  which  being  multiplied  by  3  gives  28.8 

Logarithm  of  45263  required,  4.655743 

EXAMPLE  2.     Required  the  logarithm  of  75893G.     Thus— 
The  logarithm  of  75S900  is  5.880185 

The  difference  D  is  57,  which,  being  multiplied  by  36,  gives          20.52 

Logarithm  of  758936  required,  5.880205 

NOTE.  This  process  of  finding  the  logarithms  of  large  numbers,  supposes  that 
they  increase  in  ihe  same  ratio  as  their  numbers,  which  is  not  strictly  true, 
though  sufficiently  near  the  truth  for  general  practice.  It  may  be  remarked, 
however,  that  these  ratios  approach  that  of  equality,  the  larger  the  numbers, 
and  the  less  they  differ  from  each  other. 

The  column  marked  D,  contains  the  average  mean  differences  of  the 
ten  logarithms  against  which  t-hey  stand,  and,  consequently,  do  not  al- 
ways correspond  exactly  to  each  of  the  differences,  taken  separately; 


APPENDIX.  153 

wherefore,  when  great  accuracy  is  required,  it  may  be  necessary,  par- 
ticularly in  the  first  part  of  the  table,  to  work  by 

PROBLEM  V. —  To  find  the  logarithm  of  a  number  consisting  of  six 
or  seven  figures, 

RULE.  Find  the  logarithm  of  the  first  four  figures,  as  before,  and  take 
the  difference  between  this  logarithm  and  the  next  greater,  in  the  table ; 
multiply  this  difference  by  the  remaining  figures  of  the  given  number; 
reject,  from  the  right  of  the  product,  as  many  figures  as  you  multiply 
by,  and  add  what  is  left  to  the  logarithm  before  found;  this  sum  being 
fitted  with  a  proper  index,  will  be  the  logarithm  required. 

EXAMPLE.     Required  the  logarithm  of  4526375. 

To  the  first  four  figures,  add  as  many  ciphers  as  there  are  other  fig- 
ures in  the  proposed  number,  then  find  the  logarithm,  which  substract 
from  the  next  greater.  Thus — 

The  next  greater  number  is  4527000      and  its  log,  is  6.655810 
given  number        4526000  «         6.655715 

diff.  of  numbers,          1000      diff.  of  logs.  95 

multiply  by  the  other  figures  of  the  given  number        375 

for  the  proportional  part  to  be  added  35.625 

to  the  log.,  of  the  first  part  6.655715 

and  it  gives  the  log.  of  4526375,  required.  6.655750 

PROBLEM  VI.—  To  find  the  logarithm  of  a  fraction. 

RULE.  Substract  the  logarithm  of  the  denominator  from  that  of  the 
numerator,  or,  reduce  the  fraction  to  a  decimal,  and  take  out  the  loga- 
rithm as  for  a  whole  number,  fitting  it  with  a  proper  index. 

EXAMPLE.     Required  the  logarithm  of  f,  or  .75. 

The  log.  of  the  numerator  (3)  is  0.477121 

of  the  denominator  (4)  is  0.602060 

Log.  of  |,  or  .75.  Answer,— 1 .875061 

PROBLEM  VII. —  To  find  the  Noiural  Nmnber  belonging  to  any 
logarithm. 

RULE  1.  If  the  logarithm  be  found  within  the  limits  of  the  table  ; 
that  is,  if  its  index  do  not  exceed  3;  then,  neglecting  the  index,  look 
down  in  the  column  of  logarithms,  under  0,  for  the  two  or  three  first 
figures  of  your  given  logarithm,  and  if  you  exactly  find  all  the  figures 
of  the  given  logarithm  in  that  column,  you  will  have  the  correspond- 
ing number  in  the  adjoining  column,  on  the  left. 

RULE  2.  If  the  logarithm  be  not  found,  exactly,  in  the  column  under 
0,  look  through  the  other  columns,  on  the  right,  till  you  find  it  exactly, 
or  very  nearly ;  and  in  the  column  of  numbers  directly  against  it,  you 
will  have  the  first  three  figures  of  the  number  sought,  to  which  join  the 
figure  at  the  top  of  the  column,  in  which  the  logarithm  was  found,  and 
you  will  have  the  number  required. 


154  APPENDIX. 

NOTE.  When  the  number  4s  found,  you  must  point  off  decimals  from  it,  or  annex 
ciphers  to  it,  if  necessary,  to  make  it  correspond  with  the  Index  of  your  loga- 
rithm, as  already  taught. 

EXAMPLES. 

Logarithms.  Numbers. 

3.880585  7596 

2.402089  252.4 

1.514946  32.73 

0.629919  4.265 

—1.811508  .6479 

—2.907680  .08085 

—3.962454  .009172 

When  great  accuracy  is  required,  and  the  given  logarithm  is  not 
exactly,  or  very  nearly,  found  in  the  table,  it  will  be  necessary  to  re- 
verse the  rule,  under  Problem  IV.  or  V.  Thus  : 

ROLE  3.  From  the  given  logarithm  substract  the  next  less,  in  the 
table  ;  annex  to  the  difference  as  many  ciphers  as  you  wish  the  num- 
ber of  figures  in  the  answer  to  exceed  four.  Then  divide  this  differ- 
ence by  the  common  difference  in  the  side  column  D,  and  annex  the 
quotient  to  the  natural  number  belonging  to  the  less  logarithm,  and  you 
will  have  the  number  required. 

EXAMPLE  1 .   Required  the  natural  number  belonging  to  the  logarithm 

3.441049 
next  less  log.  3.440909      corresponding  number    2760 


divide  by  com.  D=  157)14000(quotes 


Number  required,  2760.89 

EXAMPLE  2.  Required  the  number  corresponding  to  the  logarithm 
—3.441049. 

The  operation  in  this  example,  is  the  same  as  in  the  first.  Having 
found  the  corresponding  number,  as  before,  prefix  the  number  of  ci- 
phers indicated  by  the  negative  index,  thus,  0.00276089. 

PROBLEM  VIII. — Directions  for  taking  the  logarithmic  sines  and 
tangents,  and  the  logarithmic  co-sines  and  co-tangents,  from  the  table. 

NOTE.     Logarithmic  sines  and  tangents  are  the  logarithms  of  the  natural  sines  a'.id 
tangents,  which  represent  the  length  of  the  different  sides  of  triangles. 

RULE  1.  If  the  given  angle  is  less  than  45°,  look  for  the  degrees  at 
the  top  of  the  table,  and  the  minutes  on  the  left}  then  opposite  the  min- 
utes, and  under  the  word  sine,  at  the  head  of  the  column,  will  be  found 
the  logarithmic  sine;  under  the  word  tangent,  will  be  found  the  loga- 
rithmic tangent,  &c.,  of  the  angle  required.  Thus — 

Sine  of  12°  35' is      9.338176        Co-sine  of  21°  40'  is       9968179 
Tangent  of  38°  5'  is  9.894111     *   Co-tangent  of  9°  55'  is  10.757300 

NOTE.    The  first  figure  is  the  index,  and  the  other  figures  are  the  decimal  part  of 
the  logarithms. 

RULE  2.  If  the  given  angle  is  between  45°  and  90°,  look  for  the  de- 
grees at  the  bottom  of  the  table,  and  for  the  minutes  on  the  right;  then, 
opposite  to  the  minutes,  and  over  the  word  sine,  at  the  foot  of  the  col- 


APPENDIX.  155 

umn,  will  be  found  the  sine ;  over  the  word  tangent,  will  be  found  the 

tangent,  &c.,  of  the  angle  sought.     Thus — 
Sine  of  81C  20'  is         9.995013       Co-sine  of  89°  15'  is     8.116926 
Tangent  of  73°  25'  is  10.526081       Co-tangent  of  54°  5'  is  9.859932 

RULE  3.  If  the  given  angle  is  between  90°  and  180°  ;  substract  it  from 
180°,  and  take  out  the  tabular  sine  or  co-sine,  tangent  or  co-tangent,  of 
the  remainder.  Thus — 

Sine  of  99°  is  the  sine  of         81°     Co-s.  of  111°  55' is  the  co-s.  of  68°  5' 
Tan  gent  of  102°  is  the  tang,  of  78°     Co-t.  of  127°  8'  is  the  co-t.  of  52°  52' 

Having  thus  found  the  supplement  of  the  angle,  when  it  is  obtuse,  that 
is,  when  it  exceeds  90°,  with  this  supplement,  take  out  the' tabular  sine 
or  co-sine,  tangent  or  co-tangent,  by  RULE  1st  or  2d. 

RULE  4.  If  there  are  seconds  in  the  given  angle ;  find  the  tabular 
number  for  the  degrees  and  minutes,  as  before ;  then  multiply  the  oppo- 
site number  in  the  adjoining  column  D,  by  the  seconds,  cut  off  two  fig- 
ures from  the  right  of  the  product,  and  add  what  remains  to  the  loga- 
rithm, before  found,  for  sines  and  tangents,  but  substract  it  for  co-sines 
and  co-tangents,  and  the  sum  or  difference  will  be  the  angle  required. 
Thus— 

1.  Required  the  log.  sine  of  28°  42'  5". 

Sine  of  28°  42'  is  9.681443 

D=  384  multiplied  by  5"  =  19.20 

Sine  of  28°  42'  5"        Ans.  9.681462 

2.  Required  co-tangent  of  39°  17'  10". 

Co-tangent  of  39°  IT  is  10.087244 

D  =  430  multiplied  by  10  =  43.00 

Co-tangent  39°  IT  10"        Ans.  10.087201 

PROBLEM  IX. —  To  find  the  logarithmic  secant  or  co-secant  of  an 


RULE  1.  To  find  the  logarithmic  secant  of  an  angle :  substract  the  log- 
arithmic co-sine  of  the  same  angle  from  20. 000000. 

RULE  2.  To  find  the  logarithmic  co-secant  of  an  angle :  substract  the 
logarithmic  sine  of  the  same  angle  from  20.000000. 

PROBLEM  X. —  To  find  the  degrees  and  minutes  corresponding  to 

any  logarithmic  sine  or  tangent. 

RULE  1.  Look  in  the  column  of  the  same  name  with  what  you  wish 
to  find,  for  the  sine  or  tangent  which  is  nearest  to  the  given  one;  and 
if  the  title  be  at  the  head  of  the  column,  take  the  degrees  at  the  top  of 
the  table,  and  the  minutes  on  the  left ;  but  if  the  title  be  at  the  foot  of 
the  column,  take  the  degrees  at  the  bottom,  and  the  minutes  on  the  right. 

EXAMPLE.  Find  the  number  of  degrees  and  minutes  corresponding 
to  the  logarithmic  sine  9.673971. 

The  nearest  sine  in  the  table  is  9.673977.  The  title  of  sine  is  at  the 
head  of  the  column  in  which  the  number  is  found,  and  the  degrees  at 
the  top  of  the  page  are  28,  and  the  minutes  on  the  left  are  10.  The 
angle  required  is,  therefore,  28°  10',  neglecting  the  small  surplus  frac- 
tion of  6,  in  the  last  figure  of  the  logarithm. 


156  APPENDIX. 

When  the  given  logarithmic  sign  or  tangent  is  not  found  exactly,  or 
very  nearly,  then,  for  the  seconds, — 

RULE  2.  From  the  given  logarithm,  snbstract  the  next  less  in  the 
table,  annex  two  ciphers  to  the  remainder,  and  divide  it,  thus  augment- 
ed, by  the  tabular  difference  D,  and  the  quotient  will  be  the  number 
of  seconds  to  be  added  to  the  degrees  and  minutes  of  the  tabular  loga- 
rithm, for  sines  and  tangents,  but  which  must  be  substracted  for  co-sines 
and  co-tangents. 

EXAMPLE.    Required  the  degrees,  minutes,  and  seconds,  correspond- 
ing to  the  logarithmic  sine  of  9.759567. 
Given  logarithm  9.759567 

Next  less  in  the  table  =  9.759492  =  35°  5' 


Divide  by  tab.  diff.  300)7500(quotes=  25' 


Angle  required,=  35°  5'  25-" 


MULTIPLICATION  BY  LOGARITHMS. 

RULE.  Take  from  the  table  the  logarithms  of  all  numbers  to  be 
multiplied,  add  them  together,  and  their  sum  will  be  the  logarithm  of 
\he  product.  Then,  by  means  of  the  table,  take  out  the  natural  num- 
ber, corresponding  to  this  sum,  for  the  product  sought. 

Observe,  that  whatever  is  to  be  carried  from  the  decimal  part  of  the 
logarithm,  is  always  positive,  and  must  be  added  to  the  positive,  or  sub- 
stracted from  the  negative  index  or  indices. 

EXAMPLES. 

Numbers.         Logarithms:  Numbers.        Logarithms. 

1.  Mult.  326  2.513218  2.  Mult.8.25  0.916454 

by       85  1.929419  by     112  2.049218 

Prod.  27710               4.442637  Prod.  924.00           2.965672 
3.  Multiply  the  following  numbers  together:  3.902,   597.16,    and 
.0314728. 

Numbers.  Logarithms. 

3.902  0.591287 

597.160  2.776091 

.0314728  2.497935 


Prod.          73.3333  1.865313 

Here,  the  2  cancels  the  2,  and  the  1  to  carry,  from  the  decimal  part 
of  the  logarithms,  is  set  down. 

4.  Multiply  3.586,  and  2.1046,  and  0.8372,  and  0  0294,  all  together. 
Numbers.  Logarithms. 

3.586  0.554610 

2.1046  0.323170 

0.8372  T.922829 

0.0294  2-468347 


Prod.        0.105762  1.268956 

Here,  the  2  to  carry  cancels  the  2,  and  there  remains  the  T  to  set 
down  for  the  index  of  the  product. 


APPENDIX.  157 

In  practice,  however,  it  is  usual  to  make  all  the  indices  positive. 
This  is  done  by  adding  10  to  each  negative  index ;  observing  to  reject 
an  equal  number  from  the  final  result. 
Thus,  for  negative — 1,  we  may  put  down  positive  9. 
for  negative — 2,  we  may  put  down  positive  8. 
for  negative— 3,  we  may  put  down  positive  7,  &c. 
Because,  minus  1,  plus  10,  equals  9. 
minus  2,  plus  10,  equals  8. 
minus  3,  plus  10,  equals  7,  &c. 
5.  Repeating  the  third  example,  we  have 

Numbers.  Logarithms.  Logarithms. 

3.902  0.591287  =  0.591287 

597.160  2.776091  =  2.776091 

.0314728  ^.497935  or  8.497935 


Prod.  73.3333  1.865313  1.865313 

Here  the  sum  of  the  indices  is  11:  from  which  reject  10,  and  the 
result  is  the  same  as  before. 


COMPOUND  INTEREST  BY  LOGARITHMS. 

RULE.  Find  the  amount  of  1  dollar  for  1  year  ;  multiply  its  loga- 
rithms by  the  number  of  years ;  and  to  the  product,  add  the  logarithm 
of  the  principal.  The  sum  will  be  the  logarithm  of  the  amount  for 
the  given  time. 

From  the  amount  substract  the  principal,  and  the  remainder  will  be 
the  interest. 

EXAMPLE.  The  last  example  in  Daboll's  Arithmetic,  under  Com- 
pound Interest,  is  as  follows  : — "  What  will  50  dollars  amount  to  in  20 
years  at  6  per  cent." 

This  question  wrought  out  in  the  most  expeditious  manner  by  com- 
mon arithmetic,  would  take  the  student  scarcely  less  than  three  hours, 
and  the  final  result  would  be,  if  done  correctly, 

$160.3567736106422365941496492288974572748800. 
But,  by  logarithms,  this  sum  may  be  done  in  as  many  minutes,  and  the 
correct  answer,  in  dollars  and  cents,  obtained  with  very  few  figures. 
Thus: 

Amount  of  1  dollar  for  1  year  is  1.06        logarithm        0.0253059 
Multiply  by  the  time  20 

0.5061180 
Add  log.  of  principal  50        1.6989700 

Amount  as  above  =  $160.35,7         2.2050880 

From  the  foregoing  general  principles  of  the  nature  and  application 
of  logarithms,  are  derived  an  infinite  number  of  specific  rules,  adapt- 
ed to  particular  cases. 


OP  THE  TABLE  OP  NATURAL  SINES  AND  TANGENTS. 

To  those  who  are  unacquainted  with  logarithms,  it  will  be  interest- 
ing to  know,  that  all  the  cases  in  right  and  oblique  angled  trigonome- 
try, contained  in  this  work,  or  which  are  necessary  in  rectangular 


158  APPENDIX. 

surveying,  may,  by  the  help  of  natural  sines  and  tangents,  be  solved 
exactly  in  the  same  way,  and  with  the  same  facility,  as  he  would  solve 
a  simple  question  in  ike  Rule  of  Three.  Natural  sines  are  merely 
decimals,  bearing  the  same  pioportion  to  unity,  or  1,  that  the  corres- 
ponding number  of  degrees  and  minutes  bears  to  radius,  or  90°.  Na- 
tural tangents  bear  the  same  proportion  to  unity,  or  l,.that  the  corres- 
ponding number  of  degrees  and  minutes  bears  to  45°,  because  it  is  a 
well  known  principle,  that  the  sine  of  90°,  and  the  tangent  of  45°,  are 
each  equal  to  radius.  That  is,  1  is  assumed  as  the  natural  sine  of  90° 
in  the  table  of  natural  sines,  and  as  the  tangent  of  45°  in  the  table  of 
tangents,  and  every  other  number  in  each  of  these  tables,  is  calculated 
accordingly. 

GENERAL  RULE.  1.  State  the  question  in  every  case,  as  already 
taught:  2.  Multiply  the  second  and  third  terms  together,  and  divide 
the  ^product  by  the  first. 

The  manner  of  taking  natural  sines  and  tangents  from  the  tables,  is 
the  same  as  for  logarithmic  sines  and  tangents;  only  that  there  is  in 
the  tables,  no  column  of  differences  as  in  the  latter,  for  the  more  rea- 
dily rinding  the  odd  seconds,  when  required.  But  these  may  be  found 
by  making  a  proportion  for  the  aliquot  parts. 

There  are  some  problems  to  which  natural  tangents  afford  a  much 
more  simple  and  ready  solution,  than  any  process  by  logarithms.  The 
following  one,  in  heights  and  distances,  will  illustrate  this. 

EXAMPLE.  The  altitude  of  an  inaccessible  object  taken  at  an 
unknown  distance  from  its  base,  is  55°  547;  and  when  taken  again  at 
the  distance  of  93  feet  from  the  place  of  the  first  observation,  in  a 
direct  line  with  it,  the  altitude  is  33°  20':  Required,  the  height  of  the 
object. 

RULE.     Divide  the  difference  of  the  natural  co-tangents  of  the  an- 
gles of  elevation,  by  the  distance  between  the  stations.     Thus— 
Co-tangent  of  33°  20'  is  1.52043 
of55°54/is    .67705 

feet. 

Divide  by  the  diff.  =         .84338)93.0000(110.27  Ans. 

NOTE.    This  is  the  shortest  solution  possible,  and  perfectly  easy. 

Again  :  Given  the  latitude  and  departure,  in  transverse  sailing  or 
surveying,  to  find  the  course. 

RULE.  Divide  the  departure  by  the  latitude,  the  quotient  will  be  the 
natural  tangent  of  the  course  :  or,  divide  the  latitude  by  the  departure, 
and  the  quotient  will  be  the  co-tangent  of  the  course.  Universally, 
If  in  any  right  angled  triangle,  the  perpendicular  be  divided  by  the 
base,  the  quotient  will  be  the  tangent  of  the  angle  at  the  base  ;  and  if 
the  base  be  divided  by  the  perpendicular,  the  quotient  will  be  the  tan- 
gent of  the  angle  at  the  vertex  of  the  perpendicular. 


OP  THE  TRAVERSE  TABLE,  OR  TABLE  OF  LATITUDE  AND  DEPARTURE. 

This  is  calculated  for  degrees  and  quarters  of  degrees,  and  for  any 
distance  up  to  100  rods,  chains,  &c.;  by  which  the  northings  and 
southings,  eastings  and  westings,  made  in  a  survey,  may  be  found. 


APPENDIX.  159 

PROBLEM  XII.—  To  find  the  latitude  and  departure^  or  northing, 
<J"«c.  for  any  course  and  distance. 

If  the  course  be  less  than  45°,  look  for  it  at  the  top,  but  if  more  than 
45°,  at  the  bottom  of  the  page,  and  look  for  the  distance  in  the  right  or 
left  hand  column  ;  against  the  distance,  and  directly  under  or  over  the 
course,  stand  the  northing,  &c.  in  whole  numbers  and  decimals. 

If  the  course  be  less  than  15°,  the  northing  or  southing  will  be  great- 
er than  the  easting  or  westing;  but  if  more  than  45°,  the  easting  or 
westing  will  be  the  greatest. 

When  the  distance  exceeds  100,  take  any  two  or  more  numbers, 
which,  added  together,  will  equal  the  distance,  and  find  the  latitude 
and  departure  for  each  of  these  numbers;  add  the  several  latitudes 
together,  and  the  sum  will  be  the  whole  latitude  ;  and  so  for  the  de- 
parture. And  when  the  distance  is  in  chains  and  links,  or  whole 
numbers  and  decimals,  iind  the  latitude,  &c.  for  the  chains  or  wliole 
numbers,  and  then  for  the  links  and  decimals,  remembering  to  remove 
the  decimal  point  in  the  table  further  to  the  left,  according  to  the  given 
decimal. 

1.  Required  the  latitude  and  departure  for  45  rods,  on  a  course  N. 
15°  15'  W. 

Under  15°  15',  and  against  45,  is  43.42  for  the  northing,  and  11.84  for 
the  westing. 

2.  Required  the  latitude  and  departure  for  120  rods,  on  a  course  S. 
58°  30'  E. 

Take  one  third  of  120,  which  is  40;  against  this  number,  over  58° 
SO',  is  20.90  for  the  latitude,  and  34.11  for  the  departure.  These  mul- 
tiplied by  3  give  62.70  for  the  southing,  and  102.33  for  the  easting. 

3.  Required  the  latitude  and  departure  for  37.36  rods,  or  37  chains 
and  36  links,  on  a  course  N.  26°  45'  E. 

For  37.  Lat.  33.04  Dep.  16.65 

0.36  .32  .16 

37.36  33.36  16.81 

Northing  33.36,  Easting  16.81. 

NOTE.    When  the  minutes  are  not  15,  30,  or  45,  the  northings,  &c.  may  be  had  by 
proportion,  or  they  may  be  calculated  by  natural  sines,  or  by  trigonometry. 

PROBLEM  XIII.—  To  calculate  the  northing  or  southing,  $-c.  for 
any  course  and  distance^  by  natural  sines. 

Find  the  nat.  sine  and  co-sine  of  the  course,  and  into  each  of  these 
multiply  the  distance  ;  the  products  will  be  the  latitude  and  departure 
required. 

Required  the  latitude  and  departure  for  6  chains  and  22  links  on  a 
course  N.  38°  27',  W. 

Nat.  sine  of  38°  27',  0.62183  Nat.  co-sine,  0.78315 

6.22  6.22 

124366  156630 

124366  156630 

373098  469890 

3.8677826  4.8711930 

Answer.  Northing,  4.87.  Westing,  3.87. 


160 


APPENDIX. 


USEFUL  NUMBERS,  AND  THEIR  LOGARITHMS. 


Circumference  of  a  circle  to  diameter, 
Area  of  a  circle  to  radius, 
Surface  of  a  sphere  to  diameter, 
Circumference  of  a  circle  to  radius, 
Solid  contents  of  a  sphere  to  diameter, 
Solid  contents  of  a  sphere  to  radius, 
Square  of  3.14159265359 

Square  root  of  3.14159265359 

1-360  of  314159265359 

1-24  of  3.14159265359 

1-4  of  do.  or  area  of  cir.  todiam.  1 

365th  rootof  $1.05,  or  amount  of  $1.  for  1  day, 
365th  root  of$1.06,  oramountof  $1.  for  1  day, 
12th  root  of  $1.05,  or  amount  of  $1.  for  1  mo. 
12th  root  of  $1.06,  or  amount  of$l.  for  1  mo. 
360  degrees  expressed  in  seconds, 
Arc,  equal  to  radius,  in  degrees, 
in  minutes, 
in  seconds, 

Length  of  an  arc  of  l//=sine  of  I" 
of  2"=  sine  of  2' 
of  3"=  sine  of  3" 
of  V  =  sine  of  1' 
of  1° 

Sine  of  1° 

Mile,  reduced  to  rods, 
yards, 
feet, 
inches, 
Square  mile,  in  acres, 

square  rods, 
square  yards, 
square  feet, 
square  inches, 

Equatorial  diameter  of  the  earth,  in  miles, 

in  rods, 
in  yard 
in  feet, 
in  incl 

Circumference  of  the  Equator,  in  miles, 
in  feet, 
in  inches, 

Radius  of  Earth's  orbit,  in  miles, 
Sun's  horizontal  parallax, 
Log.  sine=tangent  of  8".5776 


ii 

Numbers. 

Logarith. 

3.14159265359 

0.4971499 

1 

6.28318530718 

0.7980799 

1 

0.52359877560 

-1.8950899 

1 

4.18879020479 

0.6220886 

)9 

9.86960440109 

0.9942997 

)9 

1.77245385091 

0.2485750 

>9 

0.00872664626 

-39408474 

39 

0.13089969390 

-1.1169387 

1 

0.78539816340 

-1.8950899 

day, 

1.00013368072 

0.00005805 

day, 

1.00015965359 

0.00006933 

mo. 

1.00407412 

0.00176577 

mo. 

1.0048675505 

0.00210882 

1296000 

6.1126050 

57.295780 

1.7581226 

3437.74677 

3.5362739 

206264.8 

5.3144251 

0.000004848 

-6.6855749 

0.000009696 

-6.9866049 

0.000014544 

-5.1626961 

0.000290888 

-4.4637261 

0017453293 

-2.2418774 

0.017452406 

-2.2418553 

320 

2.5051500 

1760 

3.2455127 

5280 

37226340 

63360 

4.8018152 

640 

2.8061800 

102400 

5.0103000 

3097600 

6.4910254 

27.178400 

7  4452679 

4014489600  9.603G304 

les, 

7924 

3.8989445 

Is, 

2535680 

6.4040945 

ds, 

13946240  7.1444572 

t, 

41838720  76215785 

hes. 

502064640;  8.7007597 

24893.98  4.3960944 

131440217  8.1187283 

s, 

1577282608;  91979095 

95273869|  7.9789738 

8//.57760  09333658 

5.6189407 

A   TABLE 


OF 


LOGARITHMS    OF    LUMBERS 

FROM     1     TO     10,000. 


N. 
1 
2 
3 
4 
5 

Loir. 
0.000000 
0.301030 
0.477121 
0.602060 
0.698970 

N, 

20 
27 
28 
29 
30 

Lop. 
1.414973 

1.431364 
1.447158 
,462398 
.477121 

N, 
51 
52 
53 
54 
55 

.L.*.  
.  707570 
.716003 
.  724276 
.  732394 
.  740363 

N. 
76 
77 
78 
79 
80 

!** 

.880814 
.886491 
.892095 
.897627 
.903090 

6 
7 
8 
9 
If) 

0.778151 
0.845098 
0.903090 
0,954243 
1,000000 

31 
32 
33 
34 
35 

.491362 
.505150 
.518514 
.531479 
.544068 

56 
57 
58 
59 
60 

.748188 
.755875 
.  763428 
.770852 
.778151 

81 
82 
83 
84 
85 

.908485 
.913814 
.919078 
.924279 
.929419 

li 
12 
1:3 
14 
15 

1.041393 
1.079181 
1.113943 
1.140128 
1.176091 

36 
37 
38 
39 
40 

,556303 
,568202 
.579784 
,591065 
.602060 

61 
62 
63 
64 
65 

.  785330 
.792392 
.799341 
.806180 
.812913 

86 
87 
88 
89 
90 

.934498 
.939519 
.944483 
.949390 
1.954243 

16 
17 
18 
19 
*0 

1.204120 
1.230449 
1.255273 
1,278754 
1.301030 

41 
42 
43 
44 

45 

.612784 
.  623249 
.633468 
.643453 
.653213 

66 
67 
68 
69 
70 

.819544 
.826075 
.832509 
.  838849 
.845098 

91 
92 
93 
94 
95 

1.959041 
1.963788 
1.968483 
1.973128 
1.977724 

21 
22 
23 
24 
25 

1.322219 
1.342423 
1.361728 
1.380211 
1  .397940 

46 

47 
48 
49 
50 

.662758 
.672098 
.681241 
.690196 
.698970 

71 
72 
73 
74 
75 

1.851258 
1.857333 
1.863323 
1.869232 
1.875061 

96 
97 
98 
99 
100 

1.982271 
1.986772 
1.991226 
1.995635 
2.000000 

N.  B.  In  the  following  table,  in  the  last  nine  columns  of 
each  page,  where  the  first  or  leading  figures  change  from  9's 
to  O's,  points  or  dots  are  introduced  instead  of  the  O's  through 
the  rest  of  the  line,  to  catch  the  eye,  and  to  indicate  that  from 
thence  the  annexed  first  two  figures  of  the  Logarithm  in  the 
second  column  stand  in  the  next  lower  line. 


A  TABLE  OP  LOGARITHMS  FROM   1   TO  10.000. 


N.  |   0     1  |  2    3  i  4    5    6|7|8    91  D. 

100 

000000 

0434 

0868 

1301  1734 

2166  2598;  3029|  3461 

3891 

432 

101 

4321 

4751 

5181 

5609 

6038 

6466 

6894 

7321 

7748 

8174 

428 

102 

8600 

9026 

9451 

9876 

.300 

.724 

1147 

1570 

1993 

2415 

424 

103 

012837 

3259 

3680 

4100 

4521 

4940 

5360 

5779 

6197 

6616 

419 

104 

7033 

7451 

7868 

8284 

8700 

9116 

9532 

9947 

.361 

.775 

416 

105 

021189 

1603!  2016 

2428 

2841 

3252 

3664 

4075 

4486 

4896 

412 

106 

5306 

5715!  6125 

6533 

6942 

7350 

7757 

8164 

8571 

8978 

408 

107 

9384 

9789 

.195 

.600 

1004 

1408 

1812 

2216 

2619 

3021 

404 

108 

033424 

3826 

4227 

4628 

5029 

5430 

5830 

6230 

6629 

7028 

400 

109 

7426 

7825 

8223 

8620 

9017 

9414 

9811 

.207 

.602 

.998 

396 

110 

041393 

1787 

2182 

2576 

2969 

3362 

3755 

4148 

4540 

4932 

393 

111 

5323 

5714 

6105 

6495 

6885 

7275 

7664 

8053 

8442 

8830 

389 

112 

9218 

9606|  9993 

.380 

.766 

1153 

1538  1924 

2309 

2694 

386 

113 

053078 

3463  3846 

4230 

4613 

4996 

5378 

5760 

6142 

6524 

382 

114 

6905 

7286 

7666 

8046 

8426 

8805 

9185 

9563 

9942 

.320 

379 

115 

060698 

1075 

1452 

1829 

2206 

2582 

2958 

3333 

3709 

4083 

376 

116 

4458 

4832 

5206 

5580 

5953 

6326 

6699 

7071 

7443 

7815 

372 

117 

8186 

8557 

8928 

9298 

9668 

..38 

.407 

.776 

1145 

1514 

369 

118 

071882 

2250 

2617 

2985 

3352 

3718 

4085 

4451 

4816 

5182 

366 

119 

5547 

5912 

6276!  6640 

7004 

7368 

7731 

8094 

8457 

8819 

363 

120 

079181 

9543 

9904 

.266 

.626 

.987 

1347 

1707 

2067 

2426 

360 

121 

082785 

3144 

3503 

3861 

4219 

4576 

4934 

5291 

5847 

6004 

357 

122 

6360 

6716 

7071 

7426 

7781 

8136 

8490 

8845 

9198 

9552 

355 

123 

9905 

.258 

.611 

.963 

1315 

1667 

2018 

2370 

2721 

3071 

351 

124 

093422 

3772 

4122 

4471 

4820 

5169 

5518 

5866 

6215 

6562 

349 

125 

6910 

7257 

7604 

7951 

8298 

8644 

8990 

9335 

9681 

..26 

346 

126 

100371 

0715 

1059 

1403 

1747 

2091 

2434 

2777 

3119 

3462 

343 

127 

3804 

4146 

4487 

4828 

5169 

5510 

5851 

6191 

6531 

6871 

340 

128 

7210 

7549 

7888 

8227 

8565 

8903 

9241 

9579 

9916 

.253 

338 

129 

110590 

0926 

1263 

1599 

1934 

2270 

2605 

2940 

3275  3609|335 

130 
131 

113943 

7271 

4277 
7603 

4611 
7934 

4944  5278  |  5611 
8265  8595.  8926 

5943 
9256 

6276 
9586 

660i 
9915 

6940 
.245 

3:33 
330 

132 

120574 

0903 

1231 

15601  1888!  2216 

2544 

2871 

3-198 

3525 

328 

133 

3852 

4178 

4504 

4830 

5156 

5481 

5806 

6131 

6456 

6781 

325 

134 

7105 

7429 

7753 

8076 

8399 

8722 

9045 

9368 

9690 

..12 

323 

135 

130334 

0655 

0977 

1298 

1619 

1939 

2260 

2580J  2900 

3219 

321 

136 

3539 

3858 

4177 

4496 

4814 

5133 

5451 

5769 

6086 

6403 

318 

137 

6721 

7037 

7354 

7671 

7987 

8303 

8618 

8934 

9249 

9564 

315 

138 

9879 

.194 

.508 

.822 

1136!  1450 

1763 

2076 

2389 

2702 

314 

139 

143015 

3327 

3639 

3951 

420314074 

4885 

5196 

5507 

5818 

311 

140 

146128 

6438 

6748 

7058 

7367|  7676 

7985 

8294 

8603 

8911 

309 

141 

9219!  9527 

9835 

.142 

.449 

.7561  1063 

1370 

1676 

1982 

307 

142 

152238 

2594 

2900 

3205 

3510 

3815 

4120 

4424 

4728 

5032 

305 

143 

5330 

5640 

5943 

6246 

6549 

6852 

7154 

7457 

7759 

8061 

303 

144 

8362 

8664 

8955 

9266 

9567 

9868!  .168 

.469 

.769 

1068 

301 

145 

161368 

1667 

1967 

2266 

2564  2863!  3l6l!  3460 

3758  4055 

299 

146 

43531  4650 

4947 

5244 

5541  i  5838J  6134 

6430 

6726 

7022 

297 

147 

7317 

7613 

7903 

8203 

8497 

8792!  9086 

9380 

9674 

9968 

295 

148 

170262 

0555 

0848 

1141 

1431 

1726  2019 

2311 

2603 

2895}  293 

149 

3186 

3478 

3769 

4060 

43ol 

4641 

4932 

5222 

5512 

58G2J  291 

150 

176091 

6381 

6670 

6959 

7248 

7536 

7825 

8113 

8401 

8689 

289 

151 

8977 

9264 

9552 

9839 

.126 

.413 

.699 

.985 

1272 

1558 

287 

152 

181844 

2129 

2415 

2700  29-85 

3270 

3555 

3839 

4123 

4407 

285 

153 

4691 

4975 

5259 

5542  5825!  6  108 

6391 

6674 

6956 

7239 

283 

154 

7521 

7803 

8084 

8366 

8647 

8928 

9209 

9490 

9771 

..51 

281 

155 

190332 

0612 

0892 

1171 

1451 

1730 

2010 

2289 

2567 

2846 

279 

156 

3125 

3403 

3681 

3959 

4237 

4514 

4792 

5069 

5346 

5623 

278 

157 

5899 

6176 

6453 

6729 

7005 

7281 

7556 

7832 

8107 

8382 

276 

158 

8657 

8932 

9206 

9481 

9755 

..29 

.303 

.577 

.850 

1124 

274 

159 

201397 

1670 

1943 

2216 

2488 

2761 

3033 

3305 

3577 

3848 

272 

N.    0     1    2  |  3  |  4 

5    6  i  7  1  8    9  1  D. 

A  TABLE  OF  LOGARITHMS  FROM   1  TO  10,000 


N.  |   0     1 

2|3|4|5|6|7|8 

9  |  D. 

160 

204120 

4391 

4663  4934  5204 

5475  1  5746 

6016 

6286 

6556 

271 

161 

6826 

7096 

7365 

7634 

7904 

8173 

8441 

8710 

8979 

9247 

269 

102 

9515 

9783 

..51 

.319 

.586 

.853 

1121 

1388 

1654 

1921 

267 

163 

212188 

2454 

2720  2986 

3252 

3518 

3783 

4049 

4314 

4579 

266 

164 

4844 

5109 

5373!  5638 

5902 

6166 

6430 

6694 

6957 

7221 

2o4 

165 

7484 

7747 

8010J  8273 

8536 

8793 

9060 

9323 

9585 

9846 

262 

166 

220108 

0370 

063110892 

1153 

1414 

1675 

1936 

2196 

2456 

261 

167 

2716 

2976 

3236  j  3496 

3755 

4015 

4274 

4533 

4792 

5051 

259 

168 

5309 

5568 

5826i  6084 

6342 

6600 

6858 

7115 

7372 

7630 

258 

169 

7887  8144 

8400  8657 

8913 

9170 

9426 

9682 

9938 

.193 

256 

170 

230449 

0704 

0960 

1215 

1470 

1724 

1979 

2234 

2488 

2742 

254 

171 

2996 

3250 

3504 

3757 

4011 

4264 

4517 

4770 

5023 

5276 

253 

172 

5528 

5781 

6033  j  6235 

6537 

6789 

7041 

7292 

7544 

7795 

252 

173 

8046 

8297 

8548  1  8799 

9049 

9299 

9550 

9800 

..50 

.300 

250 

174 

240549 

0799 

1048 

1297 

1546 

1795 

2044 

2293 

2541 

2790 

249 

175 

3038 

3286 

3534 

3782 

4030 

4277 

4525 

4772 

5019 

5266 

248 

176 

5513 

5759 

6006 

6252 

6499 

6745 

6991 

7237 

7482 

7728 

246 

177 

7973 

8219 

8464 

8709 

8954 

9198 

9443 

9687 

9932 

.176 

245 

178 

250420 

0664 

0908 

1151 

1395 

1638 

1831 

2125 

2368 

2610 

243 

179 

2853 

3096 

3338 

3580 

3822 

4064 

4306 

4548 

4790 

5031 

242 

180 

255273 

5514 

5755 

5996 

6237 

6477 

6718 

6958 

7198 

7439 

241 

181 

7679 

7918 

8158 

8398 

8637 

8877 

9116 

9355 

9594 

9833 

239 

182 

260071 

0310 

0548 

0787 

1025 

1263 

1501 

1739 

1976 

2214 

238 

183 

2451 

2688 

2925 

3162 

3399 

3636 

3873 

4109 

4346 

4582 

237 

184 

4818 

5054 

5290 

5525 

5761 

5996 

6232 

6467 

6702 

6937 

235 

185 

7172 

7406 

7641 

7875 

8110 

8344 

8578 

8812 

9046 

9279 

234 

186 

9513 

9746 

9980 

.213 

.446 

.679 

.912 

1144 

1377 

1609 

233 

187 

271842 

2074 

2306 

2538 

2770 

3001 

3233 

3464 

3696 

3927 

232 

188 

4158 

4389 

4620 

4850 

5081 

5311 

5542 

5772 

6002 

6232 

230 

189 

6462 

6692 

6921 

7151 

7380 

7609 

7838 

8067 

8296 

8525 

229 

190 

278754 

8982 

9211 

9439 

9667 

9895 

.123 

.351 

.578 

.806 

228 

191 

281033 

1261 

1488 

1715 

1942 

2169 

2396 

2622 

2849 

3075 

227 

192 

3301 

3527 

3753 

3979 

4205 

4431 

4656 

4882 

5107 

5332 

226 

193 

5557 

5782 

6007 

6232 

6456 

6681  6905 

7130 

7354 

7578 

225 

194 

7802 

802b 

8249 

8473 

8696 

8920 

9143 

9366 

9589 

9812 

223 

195 

290035 

0257 

0480 

0702 

0925 

1147 

1369 

1591 

1813 

2034 

222 

196 

2256 

2478 

2699 

2920 

3141 

3363 

3584 

3804 

4025 

4246 

221 

197 

4466 

4687 

4907 

5127 

5347 

5567 

5787 

6007 

6226 

6446 

220 

198 

6665 

6884 

7104 

7323 

7542 

7761 

7979 

8198 

8416 

8635 

219 

199 

8853 

9071 

9289 

9507 

9725 

9943 

.161 

.378 

.595 

.813 

218 

200 

301030 

1247 

1464 

1681 

1898 

2114 

2331 

2547 

2764 

2980 

217 

201 

3196 

3412 

3328 

3844 

4059 

4275 

4491 

4706 

4921 

5136 

216 

202 

5351 

5560  i  5781 

5996 

6211 

6425 

6639 

6854 

7068 

7282 

215 

203 

7496 

77i<; 

7924 

8137 

8351 

8564 

8778 

8991 

9204 

9417 

213 

204 

9630 

9843 

..56 

.268 

.481 

.693 

.906 

1118 

1330 

1542 

212 

205 

311754 

1966 

2177 

2389 

2600 

2812 

3023 

3234 

3445 

3656 

211 

206 

3867 

4078 

4289 

4499 

4710 

4920 

5130 

5340 

5551 

5760 

210 

207 

5970 

6180 

6390 

6599 

6809 

7018 

7227 

7436 

7646 

7854 

209 

208 

8063 

8272 

8481 

8689 

8898 

9109 

9314  9522 

9730 

9938 

208 

209 

320146 

0354 

0562 

0769 

0977 

1184 

1391 

1598 

1805 

2012 

207 

210 

322219 

2426 

2633 

2339 

3046 

3252 

3458 

3665 

3871 

4077 

206 

211 

4282 

4488 

4694 

4899 

5105 

5310 

5516 

5721 

5926 

6131 

205 

212 

6336 

6541 

6745 

6950 

7155 

7359 

7563!  7767 

7972 

8176 

204 

213 

8380 

8583 

8787 

8991 

9194 

9398 

960  li  9805 

..8 

.211 

203 

214 

330414 

0617 

0319 

1022 

1225 

1427 

1630  1832  2034 

2236 

202 

215 

2438 

2640 

2842 

3044 

3248 

3447 

3649  3850  4051 

4253 

202 

216 

4454 

4655 

4856 

5057  5257 

5458 

5658  5859!  6059 

6260 

201 

217 

6460 

66601  6860|  7060 

7260 

7459 

7659|  7853|  8058 

8257 

200 

218 

8456 

8656 

8855!  9054 

9253 

9451 

9650!  9819:  ..47 

.246 

199 

219 

340444 

0642 

0841'  1039 

1237  1435 

1632  1830'  2028 

2225 

198 

N.  |   0   |  1    2'3|4|5 

6 

7  I  8 

9  I  D. 

A  TABLE  OF  LOGARITHMS  FROM  1  TO  10,000. 


N. 

0     1  {  2  |  3  |  4 

5  |  6    7    8 

9 

D. 

220 

221 

342423 
4392 

2620 
4589 

2817 

4785 

3014 
4981 

3212 
5178 

3409 
5374 

3606 
5570 

3802]  3999 
5766  5962 

4196)  197 
6  157|  196 

222 

6353 

6549 

6744 

6939 

7135 

7330 

7525 

7720!  7915 

8110 

195 

223 

8305 

8500 

8694 

8889 

9083 

9278 

9472 

9666  9880 

..54 

194 

224 

350248  0442 

0636 

0829 

1023 

1216 

1410  1603 

1798 

1989 

193 

225 

2183  2375 

2568 

2761 

2954 

3147 

333913532 

3724 

3916 

193 

226 

227 

41081  4301 
6026  6217 

4493 
6408 

4685 
6599 

4876  5068 
67901  6981 

6360  5452  5643]  5834!  192 
7172!  736317554  7744!  191 

228 

7935  8125 

8316 

8506  8696 

8886 

9076!  9266  9456 

9646 

190 

229 

9835 

..25 

.215 

.404 

.593 

.783 

.972;  1161 

1350 

1539 

189 

230 

361728 

1917 

2105 

22941  2482 

2671 

2859;  3048 

3236 

3424 

188 

231 

3612 

3800 

3988 

4176  4363 

4551 

4739  4i>25 

5113 

5301  188 

232 

5488 

5675 

5862 

6049  6236 

6423 

6610  67961  69S3 

7169!  187 

233 

7356 

7542 

7729 

7915 

8101 

8287 

8473  8659!  8845 

9030  186 

!234 

9216 

9401 

9587 

9772 

9958 

.143 

.328 

.513 

.698 

.883 

185 

235 

371068 

1253 

1437 

1622  1806 

1991 

2175 

2360 

2544 

2728 

184 

236 

2912 

3096 

3280 

3484  3647 

3331 

4015  41  98 

4382 

4565 

184 

237 

4748 

4932 

5115 

5298 

5481 

5664 

5846  6029 

6212 

6394  183 

238 

6577 

6759 

6942 

7124 

7306 

7488 

7670 

7852 

8034 

8210 

182 

239 

8398 

8580 

8761 

8943 

9124 

9306 

9487 

9668 

9849 

..30 

181 

240 

380211 

0392 

0573 

0754 

0934 

1115 

1296 

1476 

1656 

1837!  181 

241 

2017 

2197 

2377 

2557 

2737 

2917 

3097 

3277 

3456 

3636 

180 

242 

3815 

3995 

4174 

4353*4533 

4712 

4891 

5070 

5249 

5428 

179 

243 

5606 

5785 

5964 

6l42r6321 

6499 

66771  6856 

7034 

7212 

178 

244 

7390 

7568 

7746 

7923 

8101 

8279 

8456 

8634 

881  ij  8989 

178 

245 

9166 

9343 

9520 

9698 

9875 

..51 

.228 

.405 

.582 

.759 

177 

246 

390935 

1112 

1288 

1464 

1641 

1817 

1993 

2169 

2345 

2521 

176 

247 

2697 

2873 

3048 

3224 

3400 

3575 

3751 

3926 

4101 

4277 

176 

248 

4452  4627 

4802 

4977 

5152 

5326 

5501 

5676 

5850!  6025 

175. 

249 

6199 

6374 

6548 

6722 

6896 

7071 

7245 

7419  7592]  7766 

174 

250 

397940 

8114 

8287 

84611  8634 

8808 

8981 

9154 

9328 

9501 

173 

251 

9674 

9847 

..20 

.192!  .365 

.538 

.711 

.883 

1056 

1228 

173 

252 

401401 

1573 

1745 

19171  2089 

2261 

2433 

2605 

2777  2949 

172 

253 

3121 

3292 

3464 

3635|  3807 

3978 

414S 

432(> 

4492 

4663 

171 

254 

4834 

5005 

5176 

53461  55.7 

5688 

5858]  6029 

6199 

6370 

171 

255 

6540 

6710 

688  f 

7051  7221 

7391 

7561  7731 

79>01  8070 

170 

256 

8240 

8410 

8579 

8749!  8918 

9087 

9257  9426  9595 

97G4 

169 

257 

9933 

.102 

.271 

.440!  .609 

.777 

.946  1114 

1283 

1451 

169 

258 

411620 

1788 

1956 

2124'  2293 

2461 

2G29  2796 

2964 

3132 

168 

259 

3300 

3467 

3635 

3803  j  3970 

4  137 

4305  4472  4639 

4806 

167 

260 

41-&73 

5140 

5307 

5474  5641 

5808 

5974  6141 

6308 

6474 

167 

261 

6641 

6807 

6973 

7139!  7306 

7472  7638  1  7804 

7970 

8135!  166 

262 

8301 

8467 

8633 

8798J  8964 

9129  9295  9460  9825 

9791  !  165 

263 

9956 

.121 

.286 

.451  .616 

.781  .945  1110  1275 

1439 

165 

264 

421604 

17G8 

1933 

20971  2261 

2428  25W)  2754  2918 

30S2 

164 

265 

3246 

3410 

3374 

37371  3901 

4065  4228  j  4392  4555 

4718 

164 

266 

4882 

5045 

5208 

5371  !  5534 

5697]  5860  6023  6186 

6349 

163 

267 

6511 

6674 

6836  6U99!  7161 

7324'  7489 

7648 

7811 

7973 

162 

268 

8135 

8297 

8459  8621 

8783  8944  9106 

9268 

9421) 

9591!  162 

263 

9752 

9914 

..75  .236 

.398  .559!  .720  .881 

1Q42 

1203  161 

270 

431364  1525  1685  1846!  2007 

2167]  2328!  2488  2649 

2809 

161 

271 

2969  3130!  3290  3450  3610 

3770  3930  4090  4249 

44091  160 

272 

4569J  4729J  4888  5048  5207|  5367!  5526 

5685  5844 

6004!  159 

273 

6163!  6322]  6481  6640  6798  6957  7116 

7275.  7433 

7592 

159 

274 

7751|  7909  8067  8226  8384  8542  8701 

8859  i  9017 

9175  158 

275 

9333  9491  96481  9806^  9964;  .122  .279 

.437  ,594 

.752]  158 

276 

440909  1066  1224  13811  1538!  1695  !  1852  2009  2166 

2323 

157 

277 

278 

2480|  ?637  2793 
4045  4201  14357 

29501  3106!  3263  3419  3576;  3732 
4513:  4689  4825  493  !•'  5137;  5293 

3889 
5449 

157 
156 

279 

5604  57601  5915  6071  6226  6382  6537  fi6J>3  6848 

7003 

155 

N. 

0     1  |  2  |  3    4    5  t  6 

7    8 

9 

D.T 

A  TABLE  OF  LOGARITHMS  FROM   1   TO  10,000. 


N. 

0     1    2  |  3  t  4 

6    6  f  7  j  8  |  9  |  D. 

280 

447158 

7313|  7468 

7623 

7778|  T933 

8088 

8242,  8397 

8552 

155 

281 

8706 

8861 

9015 

9170 

9324 

9478 

9633 

9787  9941 

..95 

154 

282 

450249 

0403 

0557 

0711 

0865  1018 

1172 

1326  1479 

1633 

154 

283 

1786 

1940 

2093 

2247 

2400  2553 

2706 

2859  3012 

3165 

153 

284 

3318 

3471 

3624 

3777 

3930 

4082 

4235 

4387  4540 

4692 

153 

285 

4845 

4997 

5150 

5302 

5454 

5606 

5758 

5910  6062 

6214 

152 

286 

6366 

6518 

6670 

6821 

6973 

7125 

7276 

7428 

7579 

7731 

152 

287 

7882 

8033 

8184 

8336 

8487 

8638 

8789 

8940 

9091 

9242 

151- 

288 

9392 

9543 

9694 

9845 

9995i  .146 

.296 

.447 

.597 

.748 

151 

289 

460898 

1048 

1198 

1348 

1499 

1649 

1799 

1948 

2098 

2248 

150 

290 

462398 

2548 

2697 

2847 

2997 

3146 

3296 

3445 

3594 

3744 

150 

291 

3893 

4042 

4191 

4340 

4490 

4639 

4788 

4936 

5085 

5234 

149 

292 

5383 

5532 

5680 

5829 

5977 

6126 

6274 

6423 

6571 

6719 

149 

293 

6868 

7016 

7164 

7312 

7460 

7608 

7756 

7904 

8052 

8200 

148 

294 

8347 

8495 

8643 

8790 

8938 

9085 

9233 

9380 

9527 

9675 

148 

295 

9822 

9969 

.116 

.263 

.410  .557 

.704 

.851 

.998 

1145 

147 

296 

471292 

1438 

1585 

1732 

1878 

2025 

2171 

2318 

2464 

2610 

146 

297 

2756 

2903 

3049 

3195 

3341 

3487 

3633 

3779 

3925 

4071 

146 

298 

4216 

4362 

4508 

4653  4799  4944 

5090 

5235 

5381 

5526 

146 

299 

5671 

58  1  6 

5962 

6107  6252  6397 

6542 

6687 

6832 

6976 

145 

300 

477121 

7266 

7411 

7555  7700 

7844 

7989 

8133 

8278 

8422 

145 

301 

8566 

8711 

8855 

8999 

9143 

9287 

9431 

9575 

9719 

9863 

144 

302  480007 

0151 

0294 

0438  0582 

0725 

0869 

1012 

1156 

1299 

144 

303    1443 

15S6 

1729 

1872!  2016 

2159 

2302 

2445 

2588 

2731 

143 

304 

2874 

3016 

3159 

3302!  3445 

3587 

3730 

3872 

4015 

4157 

143 

305 

4300 

4442 

4585 

472714869!  5011 

5153 

52951  5437 

5579 

142 

300 

5721 

5853 

6005 

6147  6289 

6430  6572!  6714  6855 

6997 

142 

307 

7138 

7280  7421 

7563 

7704  7845  7986 

8127  8269 

8410 

141 

308 

8551 

8692|  8833 

8974 

9114 

9255 

9396 

9537 

9677 

9818 

141 

309 

9958 

..99 

.239 

.380|  .520  j  .661 

.801 

.941 

1081 

1222 

140 

310 

491362 

1502 

1642 

1782  19221  2062 

2201 

2341 

2481 

2621 

140 

311 

2760 

2900  3040 

31791  3319 

3458 

3597 

3737)  3876!  4015 

139 

312 

4155 

4294  4433 

4572!  471114850 

4989 

5128 

5267!  5406 

139 

313 

5544 

56831  5822 

5960  6099 

62381  6376 

6515 

6653 

6791 

139 

314 

6930|  7068  7206 

7344  7483 

7621 

7759  7897 

8035 

8173 

138 

315 

8311 

8448  8586 

8724!  8802 

8999 

9137 

9275 

9412 

9550 

138 

316 

9687 

9824 

9962 

..99  .236 

.374 

.511 

.648 

.785 

.922 

137 

317 

501059 

1196 

1333 

1470  1607 

1744 

1880  2017 

2154  2291 

137 

318 

2427 

2564  2700!  2837  2973 

3109 

3246 

3382 

3518 

3655 

136 

319 

3791 

3927 

4063'  4199|  4335|  4471 

4G07 

4743 

4878 

5014 

136 

320 

505150 

5286 

5421  5557 

56931  5828 

5964 

6099  6234 

6370 

136 

321 

6505 

6640 

6776  6911 

7046 

7181 

7316 

7451 

7586 

7721 

135 

322 

7856 

7991 

8126  8260  8395 

8530 

8664 

8799 

8934 

9068 

135 

323 

9203 

9337 

9471 

9606  9740  9874 

...9  .143 

.277 

.411 

134 

324 

510545 

0679 

0813 

0947 

1081 

1215 

1349!  1482 

1616 

1750 

134 

325 

1883 

2017 

2151 

2284 

2418 

2551  2684  2818 

2951 

3084 

133 

326 

3218 

3351 

3484 

3617  3750 

3883  4016 

4149 

4282 

4414 

133 

327 

4548 

4681  4S13 

4946  5079 

5211 

5344 

5476 

5609 

5741 

133 

328 

5874 

6006 

6139 

627  ll  6403 

6535 

6668 

6800 

6932 

7064 

132 

329 

71*6 

7328 

7460 

7592 

7724 

7855 

7987 

8119 

8251 

8382 

132 

330 

518514 

8646 

8777 

8909 

9040 

9171 

9303 

9434 

9566 

9697 

131 

331 

9828 

9959 

..90 

.221 

.353  .484 

.615 

.745 

,876 

1007 

131 

332 

521138 

1269 

1400 

1530 

1661 

1792 

1922 

2053 

2183 

2314 

131 

333 

2444 

2575 

2705 

2835  2966 

3096 

3226 

3356 

348  6 

3816 

130 

334 

3746 

3876 

4006 

4136!  4266 

4396 

4526 

4656 

4785 

4915 

130 

335 

5045 

5174 

5304 

5434)  5563!  5693 

5822 

5951 

6081 

6210 

129 

336 

6339 

6469 

6598 

67271  6856  6985 

7114 

7343 

737-4 

7501 

129 

33  7 

7630 

7759 

7888 

8016 

81451  8274 

8402 

8531 

8660 

8788 

12£ 

338 
339 

8917  9045J  9174 
5302001  0328!  0456 

9302 
0584 

9430 
0712 

9559 
0840 

9687 
0968 

9815  9943 
10961  1223 

..72 
1351 

128 
128 

N.    0     1    2  I  3    4 

f  5  |  6  !  7    8    9  t  IX 

A  TABLE  OF  LOGARITHMS  FilOM   1  TO   10,000 


N.    0   |  1 

2  |  3  |  4 

5  !  6  |  7  |  8 

9  |  D. 

340 

531479 

1607 

1734 

1862 

1990 

2117 

2245 

2372 

2500 

2627 

128 

341 

2754 

2882 

3009 

3136 

3264 

3391 

3518 

3645 

3772 

3899 

127 

342 

4026 

4153 

4280 

4407 

4534 

4661 

4787 

4914 

5041 

5167 

127 

343 

5294 

5421 

5547 

5674 

5800 

5927 

6053 

6180 

6306 

6432 

126 

344 

6558 

6685 

6811 

6937 

7063 

7189 

7315 

7441 

7567 

7693 

126 

345 

7819 

7945 

8071 

8197 

8322 

8448 

8574 

8699 

8825 

8951 

126 

346 

9076 

9202 

9327 

9452 

9578 

9703 

9829 

9954 

..79 

.204 

125 

347 

540329 

0455 

0580!  0705- 

0830 

0955 

1080 

1205 

13.30 

1454 

125 

348 

1579 

1704 

1829  1953 

2078 

2203 

2327 

2452 

2576 

2701 

125 

349 

2825 

2950 

3074  3199 

3323 

3447 

3571 

3696 

ssro 

3944 

124 

350 

544068 

4192 

4316  4440 

4564 

4688 

4812 

4936 

5060 

5183 

124 

351 

5307 

5431 

5555  5678 

5802 

5925 

6049 

6172 

6296 

6419 

124 

352 

6543 

6666 

6789 

6913 

7036 

7159 

7282 

7405 

7529 

7652 

123 

353 

7775 

7898 

8021 

8144 

8267 

8389 

8512 

8G35 

8758 

8881 

123 

354 

9003 

9126 

9249'  9371  .9484 

9616 

9739 

986  1!  9984 

.106 

123 

355 

550228 

0351 

0473  0595 

0717 

0840 

0962 

1084 

1206 

1328 

122 

356 

1450 

1572 

1694  1816 

1938 

2060 

2181 

2303 

2425 

2547 

122 

357 

2668 

2790 

2911 

3033 

3155 

3276 

3398 

3519 

3640 

3762 

121 

358 

3883 

4004 

4126 

4247 

4368 

4489 

4610 

4731 

4852 

4973 

121 

359 

5094 

5215 

5336|  5457 

5578 

5699 

5820' 

5940 

6061|  6182 

121 

360 

556303 

6423 

6544  6664 

6785 

6905 

7026 

7146 

7267 

7387 

120 

381 

7507 

7627 

7748 

7868 

7988 

8108 

8228 

8349  8469 

8589 

120 

362 

8709 

8829 

8948 

9068 

9188 

9308 

9428 

9548  9667 

9787 

120 

363 

9907 

..26 

.146  .265 

.385 

.504 

.624 

.743!  .863  .982 

119 

364 

561101 

1221 

1340  1459 

1578 

1698 

1817 

1&38I  2055!  2174 

119 

365 

2293 

2412 

2531!  2650 

2769 

2887 

3006 

3125 

3244!  3362 

119 

386 

3481 

3600 

37181  3837 

3955 

4074i  4192 

4311 

4429 

4548 

119 

367 

4666 

4784 

4903  5021 

5135 

5257  5376 

5494 

5612 

5730 

118 

368 

5848 

5966 

6084  6202 

6320 

6437  0555 

6673 

6791 

6909 

118 

369 

7026 

7144 

72G2  7379 

7497 

7614J  7732 

7849  7967 

8084 

118 

370 

568202 

8319 

8436i  8554 

8671 

8788  8905 

90231  9140 

9257 

117 

371 

9374 

9491 

9608J  9725 

9842 

9959  ..76 

.19k 

.309 

.426. 

117 

372 

570543 

0660 

077G 

0893 

1010 

1126 

1243 

1359 

1476 

1592 

117 

373 

1709 

1825 

1942 

2058 

2174 

2291 

2407 

2523 

2639 

2755 

116 

374 

2872 

2938 

3104 

3220 

3336  3-152 

3568 

3684 

3800 

3915 

116 

375 

4031 

4147 

4263  4379 

4494  4610 

4726 

4841 

4957  5072 

116 

376 

5188 

5303 

5419 

5534 

5650 

5765 

5880 

599-6  6111  6226 

115 

377 

6341 

6457 

6572 

6687 

6802 

6917 

7032 

7147 

7262  7377 

115 

378 

7492 

7H07 

7722J  7836 

7951 

8066  8181 

8295 

8410  8525 

115 

379 

8639 

8754 

83681  8983 

9097 

9212 

9326 

9441 

9555 

9669 

114 

380 

579784 

989S 

..12|  .126 

.241 

.355 

.469 

.583 

.697 

.811 

114 

381 

580925 

1039 

11531  12G7 

1381 

1495 

1608 

1722 

1836 

1950 

114 

382 

20G3 

2177 

2291 

2404 

2518 

2631 

2745 

2858 

2972 

3085 

114 

383 

3199 

3312 

3426 

3539 

3652 

3765 

3879 

3992 

4105 

4218 

113 

384 

4331 

4441 

4557 

4670 

4733 

48!)6i  5009 

5122 

5235 

5348 

113 

385 

5461 

5574 

5686 

5799 

5912 

6024  6137 

6250 

6362 

6475 

113 

386 

6587 

6700 

6812 

6925 

7037 

7149  7262 

7374 

7486 

7599 

112 

387 

7711 

7823 

7935 

8047 

8160 

8272 

8384 

8496 

8608 

8720 

112 

388 

8832 

8944 

9056 

9167 

9279 

9391 

9503 

9615 

9726 

9838 

112 

389 

9950 

..61 

.173 

.284 

.396 

.507 

.619 

.730 

.842 

.953 

112 

390 

591005 

1176 

1287 

1399 

1510 

1621 

1732 

1843 

1955 

2068 

111 

391 

2177 

2288 

2399 

2510 

2621 

2732 

2843 

2954 

3064 

3175 

111 

392 

3286 

3397 

3508 

3618 

3729 

3840 

3950 

4061 

4171 

4282 

111 

393 

4393 

4503 

4614 

4724 

4834 

4945 

5055 

5165 

5276 

5386 

110 

394 

5496 

5606 

5717 

5827 

5937 

6047 

6157 

6267 

6377 

6487 

110 

395 

6597 

6707 

6817 

6927 

7037 

7146 

7256 

7366 

7476 

7586 

110 

396 

7695 

7805 

7914 

8024 

8134 

8243 

8353 

8462 

85721  8681 

110 

397 

8791 

8900 

9009 

9119 

9228 

9337 

9446 

9556 

9665,  9774 

109 

398 

9883 

9992 

.101 

.210 

.319 

.428 

.537 

.646 

.755 

.864 

109 

399 

600973 

1082 

1191 

1299 

1408 

1517 

1625 

1734 

1843 

lyM 

109 

N.  |   0   |  1 

2 

8 

4|5|6|7|8    91  D. 

A  TABLE  OF  LOGARITHMS  FKOM   I   TO   10,000. 


N.  j   0 

1    2 

3  I  4 

5    6  |  7  !  8    9   D 

400 
401 

602060 
3144 

216912277 
3253  3361 

2386,  2494 
3469!  3577 

26031 
3686 

2711 
3794 

2819 
3902 

2928 
4010 

3036 

4118 

108 
108 

402 

4226 

4334 

4442 

4550 

4658 

4766 

4874 

4982 

5089 

5197 

108 

403 

5305 

5413 

5521 

5628 

5736 

5844 

5951 

6059 

6166 

6274 

108 

404 

6381 

6489 

6596 

6704 

6811)  6919 

7026 

7133 

7241 

7348 

107 

405 

7455 

7562 

7669 

7777 

7884 

7991 

8098 

8205 

8312 

8419 

107 

406 

8526 

8633 

8740 

8847 

8954 

9061 

9167 

9274 

9381 

9488 

107 

407 

9594  9701 

9808 

9914!  ..21 

.128 

.234  .341 

.447 

.554 

107 

408 

610660!  0767 

0873 

09791  1086 

1192 

1298 

1405 

1511 

1617 

106 

409 

17231  1829 

1936 

20421  2148 

2254 

2360 

2466 

2572 

2678 

106 

476 

612784 

2890 

2996 

3102 

3207 

3313 

3419 

3525 

3630 

3736 

106 

411 

3842 

3947]  4053 

4159 

4264 

4370 

4475 

4581 

4686 

4792 

106 

412 
413 

489? 
5950 

5003  5108 
6055!  6160 

5213 
6265 

5319 
6370 

5424 
6476 

5529 
6581 

5634 
6686 

5740 
6790 

5845 
6895 

105 
105 

414 
415 

416 

7000 
8048 
9093 

7105  72101  7315J  7420 

8153i  8257)8362  8466 
9198|  9302J9406  9511 

7525 
8571 
9615 

7629 
8676 
9719 

7734 

8780 
9824 

7839 
8884 
9928 

7943 
8989 
..32 

105 
105 
104 

417, 

620136 

0240 

0344  i  0448 

0552 

0656 

0760 

0864 

0968 

1072 

104 

418 

1176 

1280 

1384)  1488 

1592 

1695 

1799 

1903 

2007 

2110 

104 

419 

2214 

2318 

242112525 

2628)  2732 

2835 

2939 

3042 

3146 

104 

420 

623249 

3353  3456 

3559 

3663 

3766 

3869 

397314076 

4179 

103 

421 

4282 

"4385 

4488 

4591 

4695 

4798 

4901 

5004  5107|  5210 

103 

422 

5312 

5415 

5518)5621 

5724 

5827 

5929 

6032  6135  6238  103 

423 

6340 

6443 

6546 

6648!  6751 

6853 

6956  7053)  71611  7263 

103 

424 

7366 

7468 

7571 

7673)  7775 

7878 

7980  8082!  8185J  8287 

102- 

425 

8389 

8491 

8593 

8695  8797 

8900 

9002  9104  9206!  9308 

102 

426 

9410 

9512 

9613J  9715 

9817  9919 

..21  .123!  .224)  .326)  102  „ 

427 

630428 

0530 

0631 

0733 

0835 

0936 

1038 

1139!  12411  1342 

102 

428 

1444 

1545 

1647 

1748 

1849 

1951 

2052 

2  153  i  2255!  2356 

101 

4','.9 

2457 

2559 

2660 

2761 

2862 

2963 

3064 

3165)  3266  3367 

101 

480 

633408 

J569 

3670 

3771 

3872 

3973 

4074 

4175  4276  4376 

100 

431 
432 

4477 

5484 

4578 
5584 

4679  4779 
5685  5785 

4880)  4981 
5886)  5986 

5081  51821  5283  5383  100 
60871  6187  6287  6388  100 

433 

6488 

9588 

6688  j  6789  6889 

69891  7089  7189  7290  7390)  100 

434 

7490 

7590 

7690  7790 

7890 

79901  8090  8190  8290  83891  99 

435 

8489 

8589 

8689 

8789 

8888 

8988 

9088  9188 

9287  9387 

99 

436 

9486 

9586 

9686 

9785 

9885 

9984 

..84!  .183 

.283 

.382 

99 

437 

640481)  0581 

0680 

0779  0879 

0978 

1077i  1177 

1276 

1375 

99 

438 

1474  1573 

1672 

1771!  1871 

1970 

2069  2168 

2267)  2366 

99 

439 

2465  2563 

2662  2761 

2860 

2959 

3058  3156 

3255  3354 

99 

440 

643453  3551 

3650 

3749 

384-7 

3946 

4044 

4143 

4242!  4340 

98 

441 

4439  4537 

4636 

4734 

4832 

4931 

5029 

5127)  5226 

5324 

98 

442 

5422J  5521 

5819 

5717 

5815 

5913 

6011 

6110!  6208 

6306 

98 

443 

6404  6502 

6600  6698)  6796 

6894 

6992 

7089  7187 

7285 

98 

444 

7383  7481 

7579  7676)  7774 

7872 

7969 

8067 

8165 

8262 

98 

445 

8360  j  8458 

8555  8653  8750  8848 

8945!  9043 

9140 

9237 

97 

446 

9335  9432 

9530  i  9627 

9724 

9821 

9919 

..16 

.113 

.210 

97 

447 

650308;  0405 

0502  0599 

0696 

0793 

0890 

0987 

1084 

1181 

97 

44S 
449 

1278J  1375 
22461  2343 

1472)  1569 
24401  2536 

166(3  1762 
2633  !  2730 

1859 

2826 

1956 
2923 

2053)  2150 
3019  3116 

97 
97 

450 

6,53213!  3309 

3405  3502 

35981  3695 

3791 

3888  1  3984 

4080 

96 

451 

4177 

4273 

4369)  4465 

4562  4658 

4754 

4850!  4946 

5042 

96 

452 

5138 

5235 

53311  5427 

5523  5619 

5715 

5810 

5906 

60021  96 

453 

6098J  6194 

62901  6386 

6482  6577 

6673)  6769 

6864 

69601  96 

454 

7050  7152 

7247 

7343  7438i  7534 

7629 

7725!  7820 

7916 

96 

455 

8011  8107 

8202 

8298!  8393 

84881  8584 

8679 

8774'  8870 

95 

456 

8965  9060 

9155 

9250!  9346 

9441 

9536 

9631 

9726 

9821 

95 

457 

9916  ..1 

.106 

.201 

.296)  .391 

.486 

.581 

.676 

.771 

95 

458 

660865|  0960 

1055 

1  150 

1245 

1339I  1434 

1529 

1623 

1718 

95 

459 

1813!  1907 

2002 

2096 

2191 

228012380 

2475  2569!  26031  95 

N.  j   (I     I 

2 

3    4 

5    6  |  7  |  8 

9 

D, 

A  TABLE  OF  LOGARITHMS  FROM   J   TO   10,000. 


N. 

o  ;  i 

2  |  3  |  4  !  5 

6  1  7 

8  |  9  |  D. 

460 

662758] 

2852  [2947 

3041 

3135  3230 

3324 

3418 

3512 

3607,  94 

461 

3701 

379513889 

3983 

4078 

4172 

4266 

4360 

4454 

4548  i  94 

462 

4642 

4736 

4830 

4924 

5018 

5112 

5200 

5299 

5393 

5487 

94 

463 

5581 

5675 

5769 

5862 

5956 

6050 

6143 

6237 

6331 

6424 

94 

464 

6518 

6612 

6705 

6799 

68921  6986 

7079 

7173 

7266 

7360 

94 

165 

7453 

7546 

7640 

7733 

7826  7920 

8013 

8106 

8199 

8293 

93 

466 

8386 

8479 

8572 

8665 

87591  8852 

8945 

9038 

9131 

9224 

93 

467 

9317 

9410 

9503 

9596 

9689J  9782 

9875 

9967 

..60 

.153 

93 

468 

670246 

0339 

0431 

0524 

0617 

0710 

0802 

0895 

0988 

1080!  93 

469 

1173 

1265 

1358 

1451 

1543 

1636 

1728 

1821 

1913 

2005  93 

470 

672098 

2190 

2283 

2375 

2467 

2560 

2652 

2744 

2836 

29291  92 

471 

3021 

3113 

3205 

3297 

3390 

3482 

3574 

366613758  3850  i  92 

472 

3942 

4034 

4126 

4218 

4310 

4402 

4494 

4586  1  4677  4769  92 

473 

4861 

4953 

5045  5137 

5228 

5320 

5412 

5503)  5595J  56871  92 

474 

5778 

5870 

5962  6053 

6145 

6236 

6328 

6419  6511 

66021  92 

475 

6694 

6785 

6876 

6968 

7059 

7151 

7242 

7333 

7424 

7516 

91 

476 

7607 

7698 

7789 

7881 

7972 

8063 

8154 

8245 

8336 

8427 

91 

477 

8518 

8609 

8700 

8791 

8882 

8973 

9064 

9155 

9246 

9337 

91 

478 

9428 

9519 

9610 

9700 

9791 

9882 

9973 

..63 

.154 

.245 

91 

479 

680336 

0426 

0517 

0607 

0698 

0789 

0879 

0970 

1060 

1151 

91 

480 

681241 

1332 

1422 

1513 

1603 

1693 

1784 

1874 

1964 

2055 

90 

481 

2145 

2235 

2326 

2416 

2506 

2596 

2686 

2777 

2867 

2957 

90 

482 

3047 

3137 

3227 

3317 

3407 

3497 

3587 

3677 

3767 

3857 

90 

483 

3947 

4037 

4127 

4217 

4307 

4396 

4486 

4576 

4666 

4756 

90 

484 

4845 

4935 

5025 

5114 

5204 

5294 

5383 

5473 

5563 

5652 

90 

485 

5742 

5831 

5921 

6010 

6100 

6189 

6279 

6368 

6458 

6547 

89 

486 

6636 

6726 

6815 

6904 

6994 

7083 

7172 

7261 

7351 

7440 

89 

487 

7529 

7618 

7707 

7796 

7886 

7975 

8064 

8153 

8242 

8331 

89 

488 

8420 

8509 

8598 

8687!  8776 

8865 

8953 

9042 

9131 

9220 

89 

489 

9309 

9398 

9486 

9575 

9664 

9753 

9841 

9930 

..19 

.107 

89 

490 

690196 

0285 

0373 

0462 

0550 

0639 

0728 

0816 

0905 

0993 

89 

491 

1081 

1170 

1258 

1347 

1435 

1524 

1612 

1700 

1789 

1877 

88 

492 

1965 

2053 

2142 

2230 

2318 

2406 

2494 

2583 

2671 

2759 

88 

493 

2847 

2935 

3023 

3111 

3199 

3287 

3375 

3463 

3*51 

3639 

88 

494 

3727 

3815 

3903 

3991 

4078 

4166 

4254 

4342 

4430 

4517 

88 

495 

4605 

4693 

4781 

4868 

4956 

5044 

5131 

6219 

5307 

5394 

88 

496 

5482 

5569 

5657 

5744 

5832 

5919 

6007 

6094 

6182 

6269 

87 

497 

6356 

6444 

6531 

6618 

6706  i  6793 

6880 

6968 

7055 

7142 

87 

498 

7229 

7317 

7404 

7491 

7578  7665 

7752 

7839 

7926 

8014 

87 

499 

8101 

8188 

8275 

8362 

8449  8535 

8622 

8709 

8796 

8883 

87 

500 

698970 

9057 

9144 

9231 

9317 

9404 

9491 

9578 

9664 

9751 

87 

501 

9838 

9924 

..11 

..98 

.184 

.271 

.358 

.444 

.531 

.617 

87 

502 

700704 

0790 

0877 

0963 

1050 

1136 

1222 

1309 

1395 

1482 

86 

503 

1568 

1654 

1741 

1827  1913 

1999 

2086 

2172 

2258 

2344 

86 

504 

2431 

2517 

2603 

2689 

2775 

2861 

2947 

3033 

3119 

3205 

86 

505 

3291 

3377 

3463 

3549 

3635 

3721 

3807 

3895 

3979 

4065 

86 

506 

4151 

4236 

4322 

4408  4494 

4579 

4665 

4751 

4837 

4922 

86 

507 

5008 

5094 

5179 

5265!  5350 

5436 

5522 

5607 

5693 

5778 

86 

508 

5864 

5949 

6035 

6120 

6206 

6291 

6376 

6462 

6547 

6632 

85 

509 

6718 

6803 

6888 

6974 

7059 

7144 

7229 

7315 

7400 

7485 

85 

510 

707570 

7655 

7740 

7826 

7911 

7996 

8081 

8166 

8251 

8336 

85 

511 

8421 

8506 

8591 

8676 

-8761 

8846 

8931 

9015 

9100 

9185 

85 

512 

9270 

9355 

9440 

9524 

9609 

9694 

9779 

9863 

9948 

..33 

85 

513 

710117 

0202 

0287 

0371 

0456 

0540 

0625 

0710 

0794 

0879 

85 

514 

0963 

1048 

1132 

1217 

1301 

1385 

1470 

1554 

1639 

1723 

84 

515 

1807 

1892 

1976 

2060 

2144 

2229 

2313 

2397 

2481 

2566 

84 

516 

2650 

2734 

2818 

2902 

298613070 

3154 

3238 

3323 

3407 

84 

517 

3491 

3575 

3650 

3742 

3826 

3910 

3994 

4078 

4162J  4246 

84 

518 

4330 

4414 

4497  458114665 

4749 

4833 

4916 

5000  5084 

84 

519 

5167 

525  1 

5335  54  18  i  5502'  558  G 

5669 

5753 

5836'  5920 

84 

N.  1   0   1  1  |  2  !  3  I  4  !  5    6  |  7 

8  I  9  |  D. 

A  TABLE  OF  LOGARITHMS  FROM   1   TO   10,000. 


N.  |   0   |  1  |  2  |  3  |  4    5  |  6    7  |  8  |  9    1). 

520 

716003 

6087i  6170 

6254 

6337 

6421 

6504  6588  6671 

6754 

83 

521 

6838 

6921 

7004 

7088 

7171 

7254 

7338  7421  J7504 

75S7 

83 

522 

7671 

7754 

7837 

7920 

8003 

8086 

8169 

8253  8336 

8419 

83 

523 
524 

8502 
9331 

8585 
9414 

8668 
9497 

8751 
9580 

8834  8917 
96631  9745 

9000 

9828 

9083  9165 
991119994 

9248 
..77 

83 
83 

525 

720159 

0242 

0325 

0407 

04901  0573 

0655 

0738  i  0821 

0903 

83 

526 

0986 

1068 

1151 

1233 

1316 

1398 

1481 

1563,  1646 

1728 

82 

527 

1811 

1893 

1975 

2058 

2140 

2222 

2305 

2387,  2469 

2552 

82 

528 

2634 

2716 

2798 

2881 

2963 

3045 

3127 

3209  3291 

3374 

82 

529 

3456 

3538 

3620 

3702 

3784 

3866 

3948 

4030  4112 

4194 

82 

530 

724276 

4358 

4440 

4522 

4604 

4685 

4767i  4849i  4931 

5013 

82 

531 

5095 

5176 

5258 

5340 

5422 

5503 

5585  5667  5748 

5830 

82 

532 

5912 

5993 

6075 

6156 

6238 

6320 

6401 

6483  6564 

6646 

82 

533 

6727 

6809 

6890 

6972 

70531  7134 

7216 

7297|  7379 

7460 

81 

534 

7541 

7623 

7704 

7785 

7866 

7948 

8029 

8110  8191 

8273 

81 

535 

8354 

8435 

8516 

8597 

8678 

8759 

8841 

8922 

9003 

9084 

81 

536 

9165 

9246 

9327 

9408 

9489 

9570 

9651 

9732 

9813 

9893 

81 

537 

9974 

..55 

.136 

.217 

.298 

.378 

.459 

•540 

.621 

.702 

81 

538 

730782 

0863 

0944 

1024 

1105 

1186 

1266 

1347 

1428 

1508 

81 

539 

1589 

1C69 

1750 

1830  1911 

1991 

2072 

2152 

2233 

2313 

81 

540 

732394 

2474 

2555 

2635 

2715 

2796 

2876 

2956 

3037 

3117 

80 

541 

3197 

3278 

3358 

3438 

3518 

3598 

3679 

3759 

3839 

3919 

80 

542 

3999 

4079 

4160 

4240 

4320 

4400 

4480 

4560 

4640 

4720 

80 

543 

4800 

4880 

4960 

5040 

5120 

5200 

5279 

5359 

5439 

5519 

80 

544 

5599 

5679 

5759 

5838 

5918 

5998 

6078 

6157 

6237 

6317 

80 

545 

6397 

6476 

6556 

6635 

6715 

6795 

6874 

6954 

7034 

7113 

80 

546 

7193 

7272 

7352 

7431 

7511 

7590 

7670 

7749 

7829 

7908 

79 

547 

7987 

8067 

8146 

8225 

8305 

8384 

8463 

8543 

8622 

8701 

79 

548 

8?%1 

8860 

8939 

9018J  9097 

9177 

9256 

9335 

9414 

9493 

79 

549 

9572 

9651 

9731 

9810 

9889 

9968 

..47 

.126 

.205 

.284 

79 

550 

740363 

0442 

0521 

0600 

0678 

0757 

0836 

0915 

0994 

1073 

79 

551 

1152 

1230 

1309 

1388 

1467 

1546 

1624 

1703 

1782 

18601  79 

552 

1939 

2018 

2096 

2175 

2254 

2332 

2411 

2489 

2568 

2646 

79 

553 

2725 

2804 

2882 

2961 

3039 

3118 

3196 

3275 

3353 

3431 

78 

554 

3510 

3588 

3667 

3745 

3823 

3902 

3980 

4058 

4136 

4215 

78 

555 

4293 

4371 

4449 

4528 

4608 

46841  4762 

4840 

4919 

4997 

78 

556 

5075 

5153 

5231 

5309 

5387 

5465 

5543 

5621 

5699 

5777 

78 

557 

5855 

5933 

6011 

6089 

6167 

6245 

6323 

6401 

6479 

6556 

78 

558 

6G34 

6712 

6790 

6868 

6945 

7023 

7101 

7179 

72561  7334 

78 

559 

7412 

7489 

7567 

7645 

7722 

7800 

7878 

7955 

8033i  8110 

78 

580 

748188 

8266 

8343 

8421 

8498 

8576 

8653 

8731 

8808  8885 

77 

561 

8963 

9040 

9118 

9195 

9272 

9350 

9427 

9504 

9582  9659 

77 

562 

fi  9736 

9814 

9891 

9968 

..45 

.123 

.200 

.277!  .354|  .431 

77 

563 

750508 

0586 

0663 

0740 

0817 

0894 

0971 

1048 

11251  1202 

77 

564 

1279 

1356 

1433 

1510 

1587 

1664 

1741 

1818 

1895J  1972 

77 

565 

2048 

2125 

2202 

2279 

2356 

2433 

2509 

2586 

2663i  2740 

77 

566 

2816 

2893 

2970 

3047 

3123 

3200 

3277 

3353 

3430]  3506 

77 

567 

3583 

3660 

3736 

3813 

3889 

3966 

4042 

4119 

4195 

4272!  77 

568 

4348 

4425 

4501 

4578 

4654 

4730 

4807 

4883 

4960 

5036 

76 

569 

5112 

5189 

5265 

5341 

5417 

5494 

5570 

5646 

5722 

5799 

76 

570 

755875 

5951 

6027 

6103 

6180 

6256 

6332 

6408 

6484 

6560 

76 

571 

6636 

6712 

6788 

6864 

6940 

7016 

7092 

7168 

7244 

7320 

76 

572 

7396 

7472 

7548 

7624 

7700 

7775 

7851 

7927 

8003 

8079 

76 

573 

8155 

8230 

8306 

8382 

8458 

8533 

8609 

8685 

8761 

8836 

76 

574 

8912 

8988 

9063 

9139 

9214 

9290 

9366 

9441 

9517 

9592 

76 

575 

9668 

9743 

9819 

9894 

9970 

..45 

.121 

.196 

.272 

.347 

75 

576 

760422 

0498 

0573 

0649  0724 

0799 

0875 

0950 

1025 

1101 

75 

577 

1176 

1251 

1326 

1402|  147T 

1552 

1627 

1702 

1778J  1853 

75 

578 

1928 

2003 

2078 

2153!  2228 

2303 

2378 

2453 

2529  2604 

75 

579 

2679 

27541  2829 

2904'  js»78l  3053'  31281  3203 

3278  3353 

75 

N. 

0 

1  1  2  |  3  |  4 

5 

fi  1  7 

8    9    D. 

A  TABLE  OF  LOGARITHMS  FROM   1   TO   10.000. 


N.  j   0   |  1  f  2  |  3  j  4    5  |  6  |  7 

8 

9  |  D. 

580 

763428  3503 

3578  3652 

3727 

3802,  3877,  3952 

4027 

4101 

75 

581 

4176 

4251 

4326  440C 

4475 

4550  4624|  4699 

4774 

484S 

75 

582 

492£ 

4998 

5072  5147 

5221 

5296 

5370  5445 

5520 

5594 

75 

583 

566fj 

5743 

5818!  5892 

5966 

6041 

6115 

619( 

6264 

6338 

74 

584 

6419 

6487 

6562 

6636 

6710!  678? 

685S 

6933 

7007 

7082 

74 

585 

7166 

7230  i  7304 

7379 

7453 

7527|  7601 

7675 

7749 

78231  74 

586 

7898 

7972 

8046 

8120  8194 

8268:  8342 

8416 

8490 

85641  74 

587 

8638 

8712 

8786 

8860  8934 

9008  9082 

9156 

9230 

930 

74 

588 

9377 

9451 

9525 

95991  9673 

9746  9820  9894 

9968 

..4 

74 

589 

770115 

0189 

0263 

0336 

0410 

0484  0557  0631 

0705 

077* 

74 

,  590 

770852 

0926 

0999!  1073 

1146 

1220  1293  1367 

1440 

151- 

74 

591 

1587 

1661 

1734 

1808 

1881 

1955  2028  2102 

2175 

2248 

73 

592 

2322 

2395 

2468 

2542 

2615 

2688  !  2762  2835 

2908 

298 

73 

593 

3055  3128 

3201 

,3274 

3348 

3421  3494 

3567 

3640 

3713 

73 

594 

3786  3860 

3933 

4006 

4079 

41521  4225 

4298 

4371 

4444 

73 

595 

4517  4590 

4663 

4736 

4809 

4882)  4955!  5028 

5100 

5173 

73 

596 

5246  5319 

5392 

5465 

5538 

5610  56831  5756 

5829 

5902 

73 

597 

5974  6047 

6120 

6193 

6265 

6338  6411 

6483 

6556 

6629 

73 

598 

670  1!  6774 

6846 

6919 

6992 

7064 

7137 

7209 

7282 

7354 

73 

599 

7427 

7499 

7572 

7644 

7717 

7789 

7862 

7934 

8006 

8079 

72 

600 

778151 

8224 

8296 

8368 

8441 

8513J  8585 

8658 

8730 

8802 

"72 

601 

8874  8947 

9019 

9091 

9163 

9236 

9308 

9380 

9452 

9524 

72 

602 

9596  9669 

9741 

9813!  9885 

9957 

..29 

.101 

.173 

.245 

72 

603 

780317 

0389 

0461 

0533 

0605 

0677 

0749 

0821 

0893 

0965 

72 

604 

1037 

1109 

1181 

1253 

1324 

1396 

1468 

1540 

1612 

1684 

72 

605 

1755 

1827 

1899 

1971 

2042 

2114 

2186 

2258 

2329 

2401 

72 

606 

2473 

2544 

2616  2688 

2759 

2831 

2902 

2974 

3046 

3117 

72 

607 

3189 

3260 

3332J  3403 

3475 

3546 

3618 

3689 

3761 

3832 

71 

608 

39041  3975 

4046 

4118 

4189 

4261 

4332 

4403 

4475 

4546 

71 

609 

4617  4689 

4760 

4831 

4902 

4974 

5045 

5116 

5187 

5259 

71 

610 

785330  5401 

5472 

5543 

5615 

5686 

5757 

5828 

5899 

5970 

71 

611 

6041  6112 

6183 

6254 

6325 

6396 

6467 

6538 

6609 

6680 

71 

612 
613 
614 

67511  6822 
7460  7531 
8168  8239 

6893 
7602 
8310 

6964 
7673 

8381 

7035 

7.744 
8451 

7106 
7815 

8522 

7177 
7885 
8593 

72481  7319 
7956  S027 
8663!  8734 

7390 

8098 
8804 

71 
71 
71 

615 

8875 

8946 

9016 

9087 

9157 

9228 

9299 

9369 

9440 

9510 

71 

616 

9581 

9651 

9722 

9792 

9863 

9933 

...4 

..74 

.144 

.215 

70 

617 

790285 

0356 

0426 

0496 

0567 

0637 

0707 

0778 

0848 

0918 

70 

618 

0988 

1059 

1129 

1199 

1269  1340 

1410 

1480  1550 

1620 

70 

619 

1691 

1761 

1831 

1901 

1971J  2041 

2111 

2181 

2252 

2322 

70 

620 

792392 

2462 

2532 

2602 

2672 

2742 

2812 

2882 

2952 

3022 

70 

621 

3092 

3162 

3231 

3301 

3371 

3441 

3511 

3581 

3651 

3721 

70 

622 

3790 

3860 

3930 

4000 

4070 

4139 

4209 

4279 

4349 

4418 

70 

623 

4488 

4558 

4627 

4697 

4767 

4836 

4906 

4976 

5045 

5115 

70 

624 

5185 

5254 

5324 

5393 

5463 

5532 

5602 

5672 

5741 

5811 

70 

625 

5880 

5940 

6019 

6088 

6158 

6227 

6297 

6366 

6436 

6505 

69 

626 

6574 

6644 

6713 

6782 

6852 

6921 

6990 

7060 

7129 

7198 

69 

627 

7268 

7337 

7406 

7475 

7545 

7614 

7683 

7752 

7821 

7890 

69 

628 

7960i  8029 

8098 

8167 

8236 

8305  8374 

8443 

8513 

8582 

69 

629 

8651 

8720 

8789 

8858 

8927 

8996  9065 

9134 

9203 

9272 

69 

630 

799341 

9409 

9478 

9547 

9616 

9685  9754 

9823 

9892 

9961 

69 

631 

8000291  0098 

0167 

0236 

0305 

D373 

0442 

0511 

0580 

0648 

69 

632 

0717J  0786 

0854 

0923 

0992!  1061 

1129 

1198 

1266 

1335 

69 

633 

1404 

1472  1541 

1609 

1678 

1747 

1815 

1884 

1952 

2021 

69 

634 

2089 

2158 

2226 

2295 

2363 

2432 

2500 

2568 

2637 

2705 

69 

635 

2774 

2842 

2910 

2979 

3047:  3116 

3184 

3252 

3321 

3389 

68 

636 

3457 

3525 

3594 

3662 

3730  i  3798 

3867 

3935 

4003 

4071 

68 

637 

4139 

4208 

4276 

4344 

441  2  l  4480  4548 

4616 

4685 

4753 

68 

638 

4821 

4889 

4957 

5025 

5093:  5161 

5229 

52'J7 

5365 

5433 

68 

639 

5501 

5569 

5637 

5705 

57731  5841 

59081  59"6 

6044 

6112 

68 

N.  |   0   |  i 

2  I  3  I  4 

5 

6    7 

8  |  9  |D. 

A  TABLE  OF  LOGARITHMS  FROM  I  TO  10,000. 


11 


N.  h  9   |  1  |  2  |  3 

4 

567 

8  |  9  1  D. 

640 

806180 

6248 

6316|  6384 

6451 

6519 

6587]  6655 

6723 

6790 

68 

641 
642 

6858 
7535 

6926 
7603 

6994  7061 
76701  7738 

7129 
7806 

7197 
7873 

7264  7332 
7941  8008 

7400 
8076 

7407 
8143 

68 

68 

643 

8211 

8279 

8346 

8414 

8481 

8549 

86161  8684 

8751 

8818 

67 

644 

8886 

8953 

9021 

9088  j  9  156 

9223 

9290  i  9358 

9425 

9492 

67 

645 

9560 

9627 

9694 

97621  9829 

9896 

9964!  ..31 

..98 

.165 

67 

646 

810233 

0300 

0367 

0434 

0501 

0569  0636  i  0703 

0770 

0837 

67 

647 

0904 

0971 

1039 

1106 

1173 

1240  1307)  1374 

1441 

1508 

67 

648 

1575 

1642 

1709 

1776 

1843 

19101  1977  2044 

2111 

2178 

67 

649 

2245 

2312 

2379 

2445 

2512 

2579 

2646  2713 

2780 

2847 

67 

650 

812913 

2980 

3047 

3114 

3181 

3247 

3314  3381 

3448 

3514 

67 

651 

3581 

3648 

3714 

3781 

3S4S 

39  14  i  398  114048 

4114 

4181 

67 

652 

4248 

4314 

4381 

4447 

4514 

4581 

4647 

4714 

4780 

4847 

67 

653 

4913 

4980 

5046 

5113 

5179 

5246 

5312 

5378 

5445 

5511 

66 

654 

5578 

5644 

5711 

5777 

5843 

5910 

5976 

6042 

6109 

6175 

66 

655 

6241 

6308 

6374 

6440 

6506 

6573 

6639 

6705 

6771 

6838 

66 

656 

6904 

6970 

7036 

7102 

7169 

7235 

7301 

7367 

7433 

7499 

66 

657 

7565 

7631 

7698 

7764 

7830 

7896 

7962 

8028 

8094 

8160 

66 

658 

8226 

8292 

8358 

8424 

8490 

8556 

8622 

8688 

8754 

8820 

66 

659 

8885 

8951 

9017 

9083 

9149 

9215 

9281 

9346 

9412 

9478 

66 

660 

819544 

9610 

9676 

9741 

9807 

9873 

9939 

...4 

..70 

".  136 

66 

661 

820201 

0267 

0333 

0399 

0464 

0530 

0595 

0861 

0727 

0792 

66 

662 

0858 

0924 

0989 

1055 

1120 

1186 

1251 

1317 

1382 

1448 

66 

663 

1514 

1579 

1645 

1710 

1775 

1841 

1906 

1972 

2037 

2103 

65 

664 

2168 

2233 

2299 

2364 

2430 

2495 

2560 

2626 

2691 

2756 

65 

665 

2822 

2887 

2952 

3018 

3083  3148 

3213 

3279 

3344 

3409 

65 

666 

3474 

3539 

3605 

3670 

3-735!  3800 

3865 

3930 

3996 

4061 

65 

667 

4126 

4191 

4256 

4321 

4386 

4451 

4516 

4581 

4646 

4711 

65 

668 

4776 

4841 

4906 

4971 

5036 

5101 

5166 

523  I 

5296 

5361 

65 

669 

5426 

5491 

5556 

5621 

5686 

5751 

5815  j  5880 

5945 

6010 

65 

670 

826075 

6140 

6204 

6269  6334 

639!) 

6464 

6528 

6593 

6658  "65 

671 
r>72 

6723 
7369 

6787 
7434 

6852 
7499 

6917  69811  7046 
7563  7628  7692 

7111 

7757 

7175 

7821 

7240 

7886 

7305  65 
7951   65 

673 

8015 

8080 

8144 

8209 

8273 

8338 

8402 

8467  8531  8595!  64 

674 
675 

8660 
9304 

8724 
9368 

8789 
9432 

8853 
9497 

8918  8982 
95611  9625 

9046 
9690 

9H1J  9175 
9754!  9818 

9239  64 
9882  64 

676 

9947 

.  .11 

.  .75 

.139 

.204)  .268 

.332 

•396!  .460 

.525  64 

677 

830589 

0653 

0717J  0781 

0845  1  0909 

•09731  1037J  1102 

1166 

64 

678 

1230 

1294 

1358 

1422 

1486  1550 

1614 

1678 

1742 

1806 

'  64 

679 

1870 

1934 

1998 

2062 

2126  2189 

2253 

2317 

2381 

2445 

64 

680 

832509 

2573 

2637  2700  1  2764  2828 

2892 

2956}  3020 

3083!  64 

681 

3147 

3211 

3275  1  33381  34021  3466 

3530 

3593|  3657 

3721   64 

682 

3784 

3848 

391213975 

40391  4103 

4166 

4230!  4294 

4357  64 

683 

4421 

4484 

4548 

4611 

4675  4739 

4802 

4866J  4929!  49<J3  64 

684 

5056 

5120 

5183 

5247 

5310  5373 

5437 

5500  5564  5627  63 

685 

5691 

5754 

5817 

5881 

5944!  6007 

6071 

01341  6197  6261  J  63 

686 

6324 

6387 

6451 

6514 

6577  6641 

6704 

67671  68301  6894:  63 

687 

6957 

7020 

7083 

71461  7210  7273 

7336 

7399  7462'  7525:  63 

688 

7588 

7652 

7715 

7778  7841  1  7904J  7967 

8030^809318166!  63 

689 

8219 

8282 

8345 

8408  8471  8534  |  8597 

8660 

8723  8786  63 

690 

838849 

8912 

8975 

90381  9101  9164  9227 

9289 

9352'!  9415  ~63 

691 

9478 

9541 

9604 

9667 

9729  .9792  9855 

9918i  998  li  .  .43  63 

692 

840106 

0169 

0232 

0294 

O357'i  0420 

0482 

0545  i  0608;  067  l!  03 

693 

0733 

0796  0859 

0921 

09841  1046 

1109 

1172  1234!  1297J  63 

694 

1359 

1422 

1485 

1547 

1610 

1672 

1735 

1797  1860|  1922  63 

695 

1  985 

2047 

2110 

2172 

2235 

2297 

2360 

2422  24841  2547  62 

6-96 

2600 

2672 

2734 

2796 

2859 

2921 

2983 

3046  3108  3170  62 

697 

3233 

3295  3357 

3420 

3482 

3544 

3606 

3669;  3751 

3793 

62 

698 

3855 

3918 

3980 

4042 

4104 

4166 

4229 

429114353 

4415 

62 

699 

4477 

4539 

4601 

4664)4726 

4788 

4850 

4912!  4974!  5036-  62 

N. 

0|l|2]3    4  |  5  |  6    7    8|9 

D. 

A  TABLE  OP  LOGARITHMS  FROM  1  TO  10,000 


N.  |   0   |  1  |  2 

3  I  4 

5 

6  |  7  |  8  |  9 

D. 

700 

845098 

5160.  5222 

5284 

5346 

5408 

5470 

5532 

5594 

5656 

62 

701 

5718 

5780 

5842 

5904 

5966 

6028 

6090 

6151 

6213 

6275 

62 

702 

6337 

6399 

6461 

6523 

6585 

6646 

6708 

6770 

6832 

6894 

62 

703 

6955 

7017 

7079 

7141 

7202 

7264 

7320 

7388 

7449 

7511 

62 

704 

7573 

7634 

7696 

7758 

7819 

7881 

7943 

8004 

8066 

8128 

62 

705 

8189 

8251 

8312 

8374 

8435 

8497 

8559 

8620 

8682 

8743 

62 

706 

8805 

8866 

8928 

8989 

9051 

9112 

9174 

9235 

9297 

9358 

61 

707 

9419 

9481 

9542 

9604 

9665 

9726 

9788 

9849 

9911 

9972 

61 

708 

850033 

0095 

0156 

0217 

0279 

0340 

0401 

0462 

0524 

0585 

61 

709 

0646 

0707 

0769 

0830 

0891 

0952 

1014 

1075 

1136 

1197 

61 

710 

851258 

1320 

1381 

1442 

1503 

1564 

1625 

1686 

1747 

1809 

61 

711 

1870 

1931 

1992 

2053 

2114 

2175 

2236 

2297 

2358 

2419 

61 

712 

2480 

2541 

2602 

2663 

2724 

2785 

2846 

2907 

2968 

3029 

61 

713 

3090 

3150 

3211 

3272 

3333 

3394 

3455 

3516 

3577 

3637 

61 

714 

3898 

3759 

3820 

3881 

3941 

4002 

4003 

4124 

4185 

4245 

61 

715 

4306 

4367 

4428 

4488 

4549 

4610 

4670 

4731 

4792 

4852 

61 

716 

4913 

4974 

5034 

5095 

5156 

5216 

5277 

5337 

5398 

5459 

61 

717 

5519 

5580 

5640 

5701 

5761 

5822 

5882 

5943 

6003 

6064 

61 

718 

6124 

6185 

6245 

6306 

6366 

6427 

6487 

6548 

6608 

6668 

60 

719 

6729 

6789 

6850 

6910 

6970 

7031 

7091 

7152 

7212 

7272 

60 

720 

857332 

7393 

7453 

7513 

7574 

7634 

7694 

7755 

7815 

7875 

60 

721 

7935 

7995 

8056 

8116 

8176 

8236 

8297 

8357 

8417 

8477 

60 

722 

.  8537 

8597 

8657 

8718 

8778 

8833 

8898 

8958 

9018 

9078 

60 

723 

9138 

9198 

9258 

9318 

9379 

9439 

9499 

9559 

9619 

9679 

60 

724  '   9739 

9799 

9859 

9918 

9978 

..38 

..98 

.158 

.218 

.278 

60 

725 

860338 

0398 

0458 

0518 

0578 

0637 

0697 

0757 

0817 

0877 

60 

726 

0937 

0996 

1056 

1116 

1176 

me 

1295 

1355 

1415 

1475 

60 

727 

1534 

1594 

1654 

1714 

1773 

1  333 

1893 

1952 

2012 

2072 

60 

728 

2131 

2191 

2251 

2310 

2370 

2130 

2439 

2549 

2608 

2668 

60 

729 

2728 

2787 

2847 

2906 

2966 

3025 

3085 

3144 

3204 

3263 

60 

730 

863323 

3382 

3442 

3501 

356  1 

3620 

3680 

3739 

3799 

3858 

59 

731 

3917 

3977  4036 

4096 

4155 

4214 

4274 

4333 

4392 

4452 

59 

732 

4511 

4570  4630 

4680 

4748 

4803 

4367 

4926 

4985 

5045 

59 

733 

5104 

5163 

5222 

5282 

5341 

5400 

5459 

5519 

5578 

5637 

59 

734 

5696 

5755 

5814 

5374 

5933 

5992 

6051 

6110 

6169 

6228 

59 

735 

6287 

6346 

6405 

64G5 

6524 

6533  6642 

6701 

6760 

6819 

59 

73  t> 

6878 

6937 

6996 

7055 

7114 

7173 

7232 

7291 

7350 

7409 

59 

737 

7467 

7526 

7585 

7644 

7703 

7762 

7321 

7880 

7939 

7998 

59 

738 

8056 

8115 

8  i  74 

8233 

8292 

8350 

8409 

8468 

8527 

8586 

59 

739 

8644 

8703 

8762 

8821 

S879 

8933 

8997 

9056 

9114 

9173 

59 

740 

869232 

9290 

9349 

9408 

91f>(i 

95*5 

0584 

9642 

9701 

9760 

59 

741 

9818 

9877 

9935 

9994 

.  .  53 

.111 

.170 

.228 

.287 

.345 

59 

742 

870404 

0462 

052  1 

0579 

063-3 

0695 

0755 

0813 

0872 

0930 

58 

743 

0989 

1017 

1106 

1164 

1223 

1281 

1339 

1398 

1456 

1515 

58 

744 

1573 

1631 

1690 

1748 

1806 

1865 

1923 

1981 

2040 

2098 

58 

745 

2156 

2215 

2273 

233  1 

2339 

2443 

2506 

2564 

2622 

2681 

58 

746 

2739 

2797 

285.) 

2913 

2972 

3930 

3088 

3146 

3204 

3262 

58 

747 

3321 

3379 

3437 

3495 

3553 

3611 

3669 

3727 

3785 

3844 

58 

748 

3902 

3960 

4018 

4076 

4134 

4192 

4250 

4308 

4366 

4424 

58 

749 

4482 

4540 

4598 

4656 

4714 

4772 

4830 

4888 

4945 

5003 

58 

750 

875061 

5119 

5177 

5235 

5293 

535  1 

5409 

5466 

5524 

5582 

58 

75] 

5640 

5698 

5756 

5813 

5371 

5929 

5987 

6045 

6102 

6160 

58 

752 

6218 

6276 

6333 

6391 

6449 

6507 

6564 

6622 

6680 

6737 

58 

753 

6795 

6853 

6910 

6968 

7026 

7083 

7141 

7199 

7256 

7314 

58 

754 

7371 

7429 

7487 

7544 

7602 

7659 

7717 

7774 

7832 

7889 

58 

755 

7947 

8004 

8062 

8119 

8177 

8234 

8292 

8349 

8407 

8464 

57 

756 

8522 

8579 

8637 

8694 

8752 

8309 

8866 

8924 

8981 

9039 

57 

757 

9096 

9153 

9211 

9268 

9325 

9383 

9440 

9497 

9555 

9612 

57 

758. 

9669 

9726 

9784 

9841 

9898 

9956 

..13 

..70 

.127 

.185 

57 

759 

880242 

0299|  0356 

0413 

0471 

0528 

0585 

0642 

0699 

0756 

57 

N. 

0   |  1    2  1  3  |  4 

5 

6  |  7  |  8  |  9  {  D. 

TABLF  OF  LOGARITHMS  FROM   1   TO   10,000. 


13 


N.    0 

1 

2  |  3 

4  I  5  |  6  |  7  |  8 

9  |  D. 

760 

880814 

0871 

0928 

0985  1042 

1099 

1156 

1213 

1271 

1328 

57 

761 

1385 

1442 

1499 

1556 

1613 

1670 

1727 

1784 

1841 

1898 

57 

762 

1955 

2012 

2069 

2126 

2183 

2240 

2297 

2354 

2411 

2468 

57 

763 

2525 

2581 

2638 

2695 

2752 

2809 

2866 

2923 

2980 

3037 

57 

764 

3093 

3150 

3207 

3264 

3321 

3377 

3434 

3491 

3548 

3605 

57 

765 

3661 

3718 

3775 

3832 

3888 

3945 

4002 

4059 

4115  4172 

57 

766 

4229 

4285 

4342 

4399 

4455 

4512 

4569 

4625 

4682  4739 

57 

767 

4795 

4852 

4909 

4965 

5022 

5078 

5135 

5192 

5248  5305 

57 

768 

5361 

5418 

5474 

5531 

5587 

5644 

5700 

5757 

58131  5870 

57 

769 

5926 

5983 

6039 

6096 

6152 

C209 

6265 

0321 

6378  6434 

56 

770 

886491 

6547 

6604 

6660 

6716 

6773 

6829 

6885 

6942 

6998 

56 

771 

7054 

7111 

7167 

7223 

7280 

7336 

7392 

7449 

7505 

7561 

56 

772 

7617 

7674 

7730 

7786 

7842 

7898 

7955 

8011 

8067 

8123 

56 

773 

8179 

8236 

8292 

8348 

8404 

8460 

8516 

8573 

8629 

8685 

56 

774 

8741 

8797 

8853 

8909 

8965 

9021 

9077 

9134 

9190 

9246 

56 

775 

9302 

9358 

9414 

9470 

9526 

9582 

9638 

9694 

9750 

9806 

56 

776 

9862 

9918 

9974 

..30 

..86 

.141 

.197 

.253 

.309 

.365 

56 

777 

890421 

0477 

0533 

0589 

0645 

0700 

0756 

0812 

0868 

0924 

56 

T78 

0980 

1035 

1091 

1147 

1203 

1259 

1314 

1370 

1426 

1482 

56 

779 

1537 

1593 

1649 

1705 

1760 

1816 

1872 

1928 

1983 

2039 

56 

780 

892095 

2150 

2206 

2262 

2317 

2373 

2429 

2484 

2540 

2595 

56 

781 

2651 

2707 

2762 

281812873 

2929 

2985 

3040 

3096 

3151 

56 

782 

3207 

3262 

3318 

3373 

3429 

3484 

3540 

3595 

3651 

3706 

56 

783 

3762 

3817 

3873 

3928 

3984 

4039 

4094 

4150 

4205 

4261 

55 

784 

4316 

4371 

4427 

4482 

4538 

4593 

4648 

4704 

4759 

4814 

55 

785 

4870 

4925 

4980 

5036 

5091 

5146 

5201 

5257 

5312 

5367 

55 

786 

5423 

5478 

5533 

5588 

5644 

5699 

5754 

5809 

5864 

5920 

55 

787 

5975 

6030 

6085 

6140 

6195 

6251  6306 

6361 

6416 

6471 

55 

788 

6526 

6581 

6636 

6692 

6747 

6802 

6857 

6912 

6967 

7022 

55 

789 

7077 

7132 

7187 

7242 

7297 

7352 

7407 

7462 

7517 

7572 

55 

790 

897627 

7682 

7737 

7792 

7847 

7902 

7957 

8012 

8067 

8122 

55 

791 

8176 

8231 

8286 

8341 

8396 

8451 

8506 

8561 

8615 

8670 

55 

792 

8725 

8780 

8835 

8890 

8944 

8999 

9054 

9109 

9164 

9218 

55 

793 

9273 

9328 

9383 

9437 

9492 

9547 

9602 

9656 

9711 

9766 

55 

794 

9821 

9875 

9930 

9985 

..39 

..94 

.149 

.203 

.258 

.312 

55 

795 

900367 

0422 

0476 

0531 

0586 

0640 

0695 

0749 

0804 

0859 

55 

796 

0913 

0968 

1022 

1077 

1131 

1186 

1240 

1295 

1349 

1404 

55 

797 

1458 

1513 

1567 

1622 

1676 

1731 

1785 

1840 

1894 

1948 

54 

798 

2003 

2057 

2112 

2166 

2221 

2275 

2329 

2384 

2438 

2492 

54 

799 

2547 

2601 

2655 

2710 

2764 

2818 

2873 

2927 

2981 

3036 

54 

800 

903090 

3144 

3199 

3253 

3307 

3361 

3416 

3470 

3524 

3578 

54 

801 

3633 

3687 

3741 

3795 

3849 

3904 

3958 

4012 

4066 

4120 

54 

802 

4174 

4229 

4283 

4337 

4391 

4445 

4499 

4553 

4607 

4661 

54 

803 

4716 

4770 

4824 

4878 

4932 

4986 

5040 

5094 

5148 

5202 

54 

804 

5256 

5310 

5364 

5418 

5472 

5526 

5580 

5634 

5688 

5742 

54 

805 

5796 

5850 

5904 

5958 

6012 

6066 

6119 

6173 

6227 

6281 

54 

806 

6335 

6389 

6443 

6497 

6551 

6604 

6658 

6712 

6766 

6820 

54 

807 

6874 

6927 

6981 

7035 

7089 

7143 

7196 

7250 

7304 

7358 

54 

808 

7411 

7465 

7519 

7573 

7626 

7680 

7734 

7787 

7841 

7895 

54 

809 

7949 

8002 

8056 

8110 

8163 

8217 

8270 

8324 

8378 

8431 

54 

810 

908485|  8539 

8592 

8646 

8699 

8753 

8807 

8860 

8914 

8967 

54 

811 

9021  9074 

9128 

9181 

9235 

9289 

9342 

9396 

9449 

9503 

54 

812 

9556 

9610 

9663 

9716 

9770 

9823 

9877 

9930 

9984 

..37 

53 

813 

910091 

0144 

0197 

0251 

0304 

0358 

0411 

0464 

0518 

0571 

53 

814 

0624 

0678 

0731 

0784 

0838 

0891 

0944 

0998 

1051 

1104 

53 

815 

1158 

1211 

1264 

1317 

1371 

1424 

1477 

1530 

1584 

1637 

53 

816 

1690 

1743 

1797 

1850 

1903 

1956 

2009 

2063 

2116 

2169 

53 

817 

2222 

2275 

2328 

2381 

2435 

2488 

2541 

2594 

2647 

2700 

53 

818 

2753  2806  2859 

2913 

2966 

3019 

3072 

3125 

3178 

3231 

53 

819 

3284  13337  1  3390 

3443 

3496 

3549 

3602 

3655 

3708 

3761 

53 

N.  i   0     1    2|3i4|5l6l7|8|9 

D. 

14 


A  TABLE  OP  LOGARITHMS  FROM   1  TO  10,000 


N.  |   0 

1  !  2  |  3  |  4" 

5  |  6  |  7  |  8  |  9  I  D. 

820 

913814  3867 

3920|  3973 

4026 

4079 

4132 

4184 

4237 

42901  53 

821 

4343 

4396 

4449 

4502 

4555 

4608 

4660 

4713 

4766 

4819 

53 

822 

4872 

4925 

4977 

5030 

5083 

5136 

5189 

5241 

5294 

5347 

53 

823 

5400 

5453 

5505 

5558 

5611 

5664 

5716 

5769 

5822 

5875 

53 

824 

5927 

5980 

6033 

6085 

6138 

6191 

6243 

6296 

6349 

6401 

53 

825 

6454 

6507 

6559 

6612 

6664 

6717 

6770 

6822 

6875 

6927 

53 

826 

6980 

7033 

7085 

7138 

7190 

7243 

7295 

7348 

7400 

7453 

53 

827 

7506 

7558 

7611 

7663 

7716 

7768 

7820 

7873 

7925 

7978 

52 

828 

8030 

8083 

8135 

8188 

8240 

8293 

8345 

8397 

8450 

8502 

52 

829 

8555 

8607 

8659 

8712 

8764 

8816 

8869 

8921 

8973 

9026 

52 

830 

919078 

9130 

9183 

9235 

9287 

9340 

9392 

9444 

9496 

9549 

52 

831 

9601 

9653 

9706 

9758 

9810 

9862 

9914 

9967 

..19 

.71 

52 

832 

920123 

0176 

0228 

0280 

0332 

0384 

0436 

0489 

0541 

0593 

52 

833 

0645 

0697 

0749 

0801 

0853 

0906 

0958 

1010 

1062 

1114 

52 

834 

1166 

1218 

1270 

1322 

1374 

1426 

1478 

1530 

1582 

1634 

52 

835 

1686 

1738 

1790 

1842 

1894 

1946 

1998 

2050 

2102 

2154 

52 

836 

2206 

2258 

2310 

2362 

2414 

2466 

2518 

2570 

2622 

2674 

52 

837 

2725 

2777 

2829 

2881 

2933 

2985  3037 

3089 

3140 

3192 

52 

838 

3244 

3296 

3348 

3399 

3451 

3503  1  3555 

3607 

3658 

3710 

52 

839 

3762 

3814 

3865 

3917 

3969 

4021 

4072 

4124 

4176 

4228 

52 

840 

924279 

4331 

4383 

4434 

4486 

4538 

4589 

4641 

4693 

4744 

52 

841 

4796 

4848 

4899 

4951 

5003 

5054 

5106 

5157 

5209 

5261 

52 

842 

5312 

5364 

5415 

5467 

5518 

5570 

5621 

5673 

5725 

5776 

52 

843 

5828 

5879 

5931 

5982 

6034 

6085 

6137 

6188 

6240 

6291 

51 

844 

6342 

6394 

6445 

6497 

6548 

6600 

6651 

6702 

6754 

6805 

51 

845 

6857 

6908 

6959 

7011 

7062 

7114 

7165 

7216 

7268 

7319 

51 

846 

7370 

7422 

7473 

7524 

7576 

76271  7678 

7730 

7781 

7832  51 

847 

7883 

7935 

7986 

8037 

8088 

8140!  8191 

8242 

8293 

8345)  51 

848 

8396 

8447 

8498 

8549 

8601 

8652  i  8703 

8754 

8805 

8857 

51 

849 

8908 

8959 

9010 

90G1 

9112 

9163 

9215 

9266 

9317 

9368 

51 

850 

929419 

9470 

9521 

9572. 

9623  9674 

9725 

9776 

9827 

9879 

51 

851 

9930 

9981 

..32 

..83 

.134!  .185|  .236 

.287 

.338 

.389 

51 

852 

930440 

0491 

0542 

0592 

0643!  0694J  0745 

07961  0847 

0898 

51 

853 

0949 

1000 

1051 

1102 

1153 

1204 

1254 

1305  1356 

1407 

51 

854 

1458 

1509 

1560 

1610 

1661 

1712 

1763 

1814 

1865 

1915 

51 

855 

1966 

2017 

2068 

2118 

2169 

2220 

2271 

2322 

2372 

2423 

51 

856 

2474 

2524 

2575 

2626 

2677 

27271  2778 

2829 

2879 

2930 

51 

857 

2981 

3031 

3082 

3133 

3183 

3234!  3285 

3335 

3386  i  3437 

51 

858 

3487 

3538 

3589 

3639 

3690 

3740)  3791 

3841 

3892 

3943 

51 

859 

3993 

4044 

4094 

4145 

4195 

4246  4296 

4347 

4397 

4448 

51 

860 

934498 

4549 

4599" 

4650 

4700 

475  li  4801 

4852 

4902 

4953 

~50 

861 

5003 

5054 

5104 

5154 

5205 

5255 

5306 

5356 

5406 

5457 

50 

862 

5507 

5558 

5608 

5658  5709 

5759 

5809 

5860 

5910 

5960 

50 

863 

6011 

6061 

6111 

6162  6212 

6262|  6313  6363 

6413 

6463 

50 

864 

6514 

6564 

6614 

6665 

6715 

67651  6815  6865 

6916 

6966 

50 

865 

7016 

7066 

7117 

7167 

7217 

726  7  1  7317J  7367 

7418 

7468 

50 

866 

7518 

7568 

7618 

7668 

7718 

7769 

7819 

7869 

7919 

7969 

50 

867 

8019 

8069 

8119 

8169 

8219 

8269  8320 

8370 

8420 

8470 

50 

868 

8520  8570 

8620 

8670 

8720 

8770  8820 

8870 

8920 

8970 

50 

869 

9020 

9070 

9120 

9170 

9220 

9270  9320 

9369 

9419 

9469 

50 

870 

939519 

9569 

9619 

966(J 

9719 

9769 

9819 

9869 

9918 

9968 

50 

871 

940018 

0068 

0118 

0168 

0218 

0267 

0317 

0367 

04J7 

0467 

50 

872 

0516 

0566 

0616 

0666 

0716 

0765  0815 

0865 

0915 

0964 

50 

873 

1014 

1064 

1114 

1163 

1213 

1263  1313 

1362 

1412 

1462 

50 

874 

1511 

1561 

1611 

1660 

1710 

1760|  1809 

1859 

1909 

1958 

50 

875 

2008 

2058 

2107 

2157 

2207 

22561  2306 

2355 

2405 

2455 

50 

876 

2504 

2554 

2603 

2653 

2702 

2752  2801 

2851 

2901 

2950 

50 

877 

3000 

3049 

3099 

3148 

3198 

3247  3297 

3346  3396 

3445 

49 

878 

3495 

3544 

3593 

3643 

3692 

3742  3791 

3841  3890 

3939 

49 

879 

3989 

4038 

4088 

4137 

4186 

4236  42851  43351  4384 

4433 

49 

N.  1   0   |  1 

2|3|4|5i6|7|8'9|D. 

A  TABLE  OF  LOGARITHMS  FROM   J    TO   10,000. 


15 


N.  1   0   |  1  |  2    3  |  4    5  |  6  |  7  |  8  |  9  1  D. 

880 

9444831  4532 

4581 

4631 

4680]  4729 

4779 

4828  4877 

4927 

49 

881 

4976  5025 

5074 

5124 

5173 

5222 

5272 

5321 

5370 

5419 

49 

882 

5469 

5518 

5567 

5616 

5665 

5715 

5764 

5813 

5862 

5912 

49 

883 

5961 

6010 

6059 

6108 

6157 

6207 

6256 

6305 

6354 

6403 

49 

884 

6452 

6501 

6551 

6600 

6649 

6698 

6747 

6796 

6845 

6894 

49 

885 

6943 

6992 

7041 

7090 

7140 

7189 

7238 

7287 

7336 

7385 

49 

886 

7434 

7483 

7532 

7581 

7630 

7679 

7728 

7777 

7826 

7875 

49 

887 

7924 

7973 

8022 

8070 

8119 

8168 

8217 

8266 

8315 

8364 

49 

888 

8413 

8462 

8511 

8560 

8609 

8657 

8706 

8755 

8804 

8853 

49 

889 

8902 

8951 

8999 

9048 

9097 

9146 

9195 

9244 

9292 

9341 

49 

890 

949390 

9439 

9488 

9536 

9585 

9634 

9683 

9731 

9780 

9829 

49 

891 

9878 

9926 

9975 

..24 

..73 

.121 

.170 

.219 

.267 

.316 

49 

892 

950365 

0414 

0462 

0511 

0560 

0608 

OG57 

0706 

0754 

0803 

49 

893 

0851 

0900 

0949 

0997 

1046 

1095 

1143 

1192 

1240 

12*9 

49 

894 

1338 

1386 

1435 

1483 

1532 

1580 

1629 

1677 

1726 

1775 

49 

805 

1823 

1872 

1920 

1969 

2017 

2066 

2114 

2163 

2211 

2260 

48 

896 

2308 

2356 

2405 

2453 

2502 

2550 

2599 

2647 

2696 

2744 

48 

897 

2792 

2841 

2889 

2938 

2986 

3034 

3083 

3131 

3180 

3228 

48 

898 

3276 

3325 

3373 

3421 

3470 

3518 

3566 

3615 

3663 

3711 

48 

899 

3760 

3808 

3856 

3905 

3953 

4001 

4049 

4098 

4146 

4194 

48 

900 

954243 

4291 

4339 

4387 

4435 

4484 

4532 

4580 

4628 

4677 

48 

901 

4725 

4773 

4821 

4869 

4918 

4966 

5014 

5062 

5110 

5158 

48 

902 

5207 

5255 

5303 

5351 

5399 

5447 

5495 

5543 

5592 

5640 

48 

903 

5688 

5736 

5784 

5832 

5880 

5928 

5976 

6024 

6072 

6120 

48 

904 

6168 

6216 

6265 

6313 

6361 

6409 

6457 

6505 

6553 

6601 

48 

905 

6649 

6697 

6745 

6793 

6840 

6888 

6936 

6984 

7032 

7080 

48 

906 

7128 

7176 

7224 

7272 

7320 

7368 

7416 

7464 

7512 

7559 

48 

907 

7607 

7655 

7703 

7751 

7799 

7847 

7894 

7942 

7990 

8038 

48 

908 

8086 

8134 

8181 

8229 

8277 

8325 

8373 

8421 

8468 

8516 

43 

909 

8564 

8612 

8659 

8707 

8755 

8803 

8850 

8898 

8946 

8994 

48 

910 

959041 

9089 

9137 

9185 

9232 

9280 

9328 

9375 

9423 

9471 

48 

911 

9518 

9566 

9614 

9661 

9709 

9757 

9804 

9852 

9900 

9947 

48 

912 

9995 

..42 

..90 

.138 

.185 

.233 

.280 

.328 

.376 

.423 

48 

913 

960471 

0518 

0566 

0613 

0661 

0709 

0756 

0804 

0851 

0899 

48 

914 

0946 

0994 

1041 

1089 

1136 

1184 

1231 

1279 

1326 

1374 

47 

915 

1421 

1469 

1516 

1563 

1611 

1658 

1706 

1753 

1801 

1848 

47 

916 

1895 

1943 

1990 

2038 

2085 

2132 

2180 

2227 

2275 

2322 

47 

917 

2369 

2417 

2464 

2511 

2559 

2606 

2653 

2701 

2748 

2795 

47 

918 

2843 

2890 

2937 

2985 

3032 

3079 

3126 

3174 

3221 

3268 

47 

919 

3316 

3363 

3410 

3457 

3504 

3552 

3599 

3646 

3693 

3741 

47 

920 

963788 

3835 

3882 

3929 

3977 

4024 

4071 

4118 

4165 

4212 

47 

921 

4260 

4307 

4354 

4401 

4448 

4495 

4542 

4590 

4637 

4684 

47 

922 

4731 

4778 

4825 

4872 

4919 

4966 

5013 

5061 

5108 

5155 

47 

923 

5202 

5249 

5296 

5343 

5390 

5437 

5484 

5531 

5578 

5625 

47 

924 

5672 

5719 

5766 

5813 

5860 

5907 

5954 

6001 

6048 

6095 

47 

925 

6142 

6189 

6236 

6283 

6329 

6376 

6423 

6470 

6517 

6564 

47 

926 

6611 

6658 

6705 

6752 

6799 

6845 

6892 

6939 

6986 

7033 

47 

927 

7080 

7127 

7173 

7220 

7267 

7314 

7361 

7408 

7454 

7501 

47 

928 

7548 

7595 

7642 

7688 

7735 

7782 

7829 

7875 

7922 

7969 

47 

929 

8016 

8062 

8109 

8156 

8203 

8249 

8296 

8343 

8390 

8436 

47 

930 

968483 

8530 

8576 

8623 

8670 

8716 

8763 

8810 

8856 

8903 

47 

931 

8950 

8996 

9043 

9090 

9136 

9183 

9229 

9276 

9323 

9369 

47 

932 

9416 

9463 

9509 

9556 

9602 

9649 

9695 

9742 

9789 

9835 

47 

933 

9882 

9928 

9975 

..21 

..68 

.114 

.161 

.207 

.254 

.300 

47 

934 

970347 

0393 

0440 

0486 

0533 

0579 

0626 

0^72 

0719 

0765 

46 

935 

0812 

0858 

0904 

095 

0997 

1044 

1090 

1137 

1183 

122S 

46 

936 

1276 

1322 

1369 

1415 

1461 

1508 

1554 

1601 

1647 

1692 

46 

937 

1740 

1786 

1832 

187S 

1925 

197 

2018 

2064 

2110 

215 

46 

938 

2203 

2249 

229S 

2342 

2388 

243 

2481 

2527 

2573 

261 

46 

3666 

2712 

2758 

280 

2851 

289 

2943 

298S 

3035 

308   46 

N.  |   0   |  1  |  2  |  3    4  [  5  |  6  |  7 

8  |  9  I  D. 

A  TABLE  OP  LOGARITHMS  FROM   1   TO  10,000. 


N. 

0|l    2 

3  I  4 

5  |  6  |  7  |  8  |  9  |  D. 

940 

973128 

31741  3220 

3266 

3313 

3359 

3405 

3451 

3497 

3543 

46 

941 

3590 

3636 

3632 

3728 

3774 

3820 

3866 

3913 

3959 

4005 

46 

942 

4051 

4097 

4143 

4189 

4235 

4281 

4327 

4374 

4420 

4466 

46 

943 

4512 

4558 

4604 

4650 

4696 

4742 

4788 

4S34 

4880 

4926 

46 

944 

4972 

5018 

5064 

5110 

5156 

5202 

5248 

5294 

5340 

5386 

46 

945 

5432 

5478 

5524 

5570 

5616 

5662 

5707 

5753 

5799 

5845 

46 

946 

5891 

5937 

5983 

6029 

6075 

6121 

6167 

6212 

6258 

6304 

46 

947 

6350 

6396 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

6763 

46 

948 

6808 

6854 

6900 

6946 

6992 

7037 

7083 

7129 

7175 

7220 

46 

949 

7266 

7312 

7358 

7403 

7449 

7495 

7541 

7586 

7632 

7678 

46 

950 

977724 

7769 

7815 

7861 

7906 

7952 

7998 

8043 

8089 

8135 

46 

951 

8181 

8226 

8272 

8317 

8363 

8409 

8454 

8500 

8546 

8591 

46 

952 

8637 

8683 

8728 

8774 

8819 

8865 

8911 

8956 

9002 

9047 

46 

953 

9093 

9138 

9184 

9230 

9275 

9321 

9366 

9412 

9457 

9503 

46 

954 

9548 

9594 

9639 

9685 

9730 

9776 

9821 

9867 

9912 

9958 

46 

955 

980003 

0049 

0094 

0140 

0185 

0231 

0276 

0322 

0367 

0412 

45 

956 

0458 

0503 

0549 

0594 

0640 

0685 

0730 

0776 

0821 

0867 

45 

957 

0912 

0957 

1003 

1048 

1093 

1139 

1184 

1229 

1275 

1320 

45 

958 

1366 

1411 

1456 

1501 

1547 

1592 

1637 

1683 

1728 

1773 

45 

959 

1819 

1864 

1909 

1954 

2000 

2045 

2090 

2135 

2181 

2226 

45 

960 

982271 

2316 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

45 

961 

2723 

2769 

2814 

2859 

2904 

2949 

2994 

3040 

3085 

3130 

45 

962 

3175 

3220 

3265 

3310 

3356 

3401 

3446 

3491 

3536 

3581 

45 

963 

3626 

3671 

3716 

3762 

3807 

3852 

3897 

3942 

3987 

4032 

45 

964 

4077 

4122 

4167 

4212 

4257 

4302 

4347 

4392 

4437 

4482 

45 

965 

4527 

4572 

4617 

4662 

4707 

4752 

4797 

4-842 

4887 

4932 

45 

966 

4977 

5022 

5067 

5112 

5157 

5202 

5247 

5292 

5337 

5382 

45 

967 

5426 

5471 

5516 

5561 

5606 

5651 

5696 

5741 

5786 

5830 

45 

968 

5875 

5920 

5965 

6010 

6055 

6100 

6144 

6189 

62341  6279 

45 

969 

6324 

6369 

6413 

6458 

6503 

6548 

6593 

6637 

6682 

6727 

45 

970 

986772 

6817 

6861 

6906 

6951 

6996 

7040 

7085 

7130 

7175 

45 

971 

7219 

7264 

7309 

7353 

7398 

7443 

7488 

7532 

7577 

7622 

45 

972 

7666 

7711 

7756 

7800 

7845 

7890 

7934 

7979 

8024 

8068. 

45 

973 

8113 

8157 

8202 

8247 

8291 

8336 

8381 

8425 

8470 

8514 

45 

974 

8559 

8604 

8648 

8693 

8737 

8782 

8826 

8871 

8916 

8960 

45 

975 

9005 

9049 

9094 

9138 

9183 

9227 

9272 

9316 

9361 

9405 

45 

976 

9450 

9494 

9539 

9583 

9628 

9672 

9717 

9761 

9806 

9850 

44 

977 

9895 

9939 

9983 

..28 

..72 

.117 

.161 

.206 

.250 

.294 

44 

978 

990339 

0383 

0428 

0472 

0516 

0561 

0605 

0650 

0694 

0738 

44 

979 

0783 

0827 

0871 

0916 

0960 

1004 

1049 

1093 

1137 

1182 

44 

980 

991226 

1270 

1315 

1359 

1403 

1448 

1492 

1536 

1580 

1625 

44 

981 

1669 

1713 

1758 

1802 

1846 

1890 

1935 

1979 

2023 

2067 

44 

982 

2111 

2156 

2200 

2244 

2288 

2333 

2377 

2421 

2465 

2509 

44 

983 

2554 

2598 

2642 

2686 

2730 

2774 

2819 

2863 

2907 

2951 

44 

984 

2995 

3039 

3083 

3127 

3172 

32.16 

3260 

3304 

3348 

3392 

44 

985 

3436 

3480 

3524 

3568 

3613 

3657 

3701 

3745 

3789 

3833 

44 

986 

3877 

3921 

3965 

4009 

4053 

4097 

4141 

4185 

4229 

4273 

44 

987 

4317 

4361 

4405 

4449 

4493 

4537 

4581 

4625 

4669 

4713 

44 

988 

4757 

4801 

4845 

4889 

4933 

4977 

5021 

5065 

5108 

5152 

44 

989 

5196 

5240 

5284 

5328 

5372 

5416 

5460 

5504 

5547 

5591 

44 

990 

995635 

5679 

5723 

5767 

5811 

5854 

5898 

5942 

5986 

6030 

44 

991 

6074 

6117 

6161 

6205 

6249 

6293 

6337 

6380 

6424 

6468 

44 

992 

6512 

6555 

6599 

6643 

6687 

6731 

6774 

6818 

6862 

6906 

44 

993 

6949 

6993 

7037 

7080 

7124 

7168 

7212 

7255 

7299 

7343 

44 

994 

7386 

7430 

7474 

7517 

7561 

7605 

7648 

7692 

7736 

7779 

44 

995 

7823 

7867 

7910 

7954 

7998 

8041 

8085 

8129 

8172 

8216 

44 

996 

8259 

8303 

8347 

8390 

8434 

8477 

8521 

8564 

8608 

8652 

44 

997 

8695 

8739 

8782 

8826 

8869 

8913 

8956 

9000 

9043 

9087 

44 

998 

9131 

9174 

9218 

9261 

9305 

9348 

9392 

9435 

9479 

9522 

44 

999    9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

9913 

9957 

43 

N.    0   |  1    2  |  3  I  4 

5  1  6  I  7 

8  |  9  |  D. 

SINES   AND   TANGENTS. 

FOR    EVERY 

DEGREE    AND    MINUTE 

OF   THE   QUADRANT. 


N.B.  The  minutes  in  the  left-hand  column  of  each  page, 
increasing  downwards,  belong  to  the  degrees  at  the  top  ;  and 
those  increasing  upwards,  in  the  right-hand  column,  belong  to 
the  degrees  below. 


18 


(0  Degree.)     A  TABLE  OP  LOGARITHMIC 


M.  |   Sine      D.   |   Cosine    D.  |   Tang.     D.   |   Cotang. 

0 

0.000000 

10.000000 

0.000000 

Iniinite. 

60 

1 

6.463726 

501  717 

000000 

00 

6.463726 

501717 

13.536274 

59 

2 

764756 

293485 

000000 

00 

764756 

293483 

235244 

58 

3 

940847 

208231 

000000 

00 

940847 

208231 

059153 

57 

4 

7.065786 

161517 

000000 

00 

7.065786 

161517 

12.934214 

56 

5 

162696 

13J968 

000000 

00 

162696 

131969 

837304 

55 

6 

241877 

111575 

9.999999 

01 

241878 

111578 

758122 

54 

7 

308824 

96653 

999999 

01 

308825 

99653 

691175 

53 

8 

366816 

85254 

999999 

01 

366817 

85254 

633183 

52 

9 

417968 

76263 

999999 

01 

417970 

76263 

582030 

51 

10 

463725 

68988 

999998 

01 

463727 

68988 

536273 

50 

11 

7.505118 

62981 

9.999998 

01 

7.505120 

62981 

12.494880 

49 

12 

542906 

57936 

999997 

01 

542909 

57933 

457091 

48 

13 

577668 

53641 

999997 

01 

577672 

53642 

422328 

47 

14 

609853 

49938 

999996 

01 

609857 

49939 

390143 

46 

15 

639816 

46714 

999996 

01 

639820 

46715 

360180 

45 

16 

667845 

43881 

999995 

01 

667849 

43882 

332151 

44 

17 

694173 

41372 

999995 

01 

694179 

41373 

305821 

43 

18 

718997 

39135 

999994 

01 

719003 

39136 

280997 

42 

19 

742477 

37127 

999993 

01 

742484 

37128 

257516 

41 

20 

764754 

35315 

999993 

01 

764761 

35136 

235239 

40 

21 

7  .  785943 

33672 

9.999992 

01 

7.785951 

33673 

12.214049 

39 

22 

806146 

32175 

999991 

01 

806155 

32176 

193845 

38 

23 

825451 

30805 

999990 

01 

825460 

30806 

174540 

37 

24 

843934 

29547 

999989 

0-2 

843944 

29549 

156056 

36 

25 

861662 

28388!   999988 

02 

861674 

28390 

138326 

35 

26 

878695 

27317    999988 

0-2 

878708 

27318 

121292 

34 

27 

895085 

26323    999987 

02 

895099 

26325 

104901 

33 

28 

910879 

25399!   999986 

0-2 

910894 

25401 

089106 

32 

29 

926119 

24538!   999985 

02 

926134 

24^40 

073866 

31 

30 

940S42 

23733  j   999983 

02 

940858 

23735 

059142 

30 

31 

7.955082 

22980 

9.999982 

02 

7.955100 

22981 

12.044900 

29 

32 

968870 

22273 

999981 

02 

968889 

22275 

031111 

28 

33 

982233 

21608 

999980 

02 

982253 

21610 

01774-7 

27 

84 

995198 

20981 

999979 

02 

995219 

20983 

004781 

26 

35 

8.007787 

20390 

999977 

02 

8.007809 

20392 

11.992191 

25 

36 

02002  1 

19831 

999976 

02 

020045 

19°-33 

979955 

24 

37 

031919 

19302 

999975 

02 

031945 

19305 

968055 

23 

38 

043501 

188011   999973 

02 

043527 

18803 

956473 

22 

39 

Or.478  i 

183251   999972 

0-2 

054801 

18327 

945191 

21 

40 

OG5776 

17872|   999971 

02 

065806 

17874 

934194 

20 

41 

8.076500 

17441!  9.9-99969 

02 

8.076531 

17444 

11.923469 

19 

42 

086955 

17031!   999968 

02 

086997 

17034 

913003 

18 

43 

097183 

16639!   999966 

02 

097217 

16642 

902783 

17 

44 

107167 

16265!   999964  03 

107202 

16268 

892797 

16 

45 

116926 

15908    999963 

03 

110963 

15910 

883037 

15 

46 

.126471 

15566 

999961 

03 

126510 

15568 

873490 

14 

47 

135810 

1523S 

999959 

03 

135851 

15241 

864149 

13 

48 

141953 

14924 

999958 

03 

144996 

14927 

855004 

12 

49 

153907 

14622 

999956 

03 

153952 

14627 

846048 

11 

a; 

162681 

14333 

999954 

03 

162727 

14336 

837273 

10 

51 

8.171280 

14054 

9.999952 

03!  8.171328 

14057 

11.828672 

9 

52 

179713 

13786 

999950 

03 

179763 

13790 

820237 

8 

53 

187985 

13529 

999948 

03 

188036 

13532 

811964 

7 

54 

196102 

13280 

999946 

03 

196156 

13284 

803844 

6 

55 

204070 

13041 

999944 

3 

204128 

13044 

795874 

5 

56 

211895 

12810 

999942 

4 

211953 

12814 

788047 

4 

57 

219581 

12587 

999940 

04 

219641 

12590 

780359 

3 

58 

227134 

12372 

999938 

04 

227195 

12376 

772805 

2 

59 

234557 

12164 

999936 

04 

234621 

12168 

765379 

1 

60 

241855 

11763 

999934 

04 

241921 

11967 

758079 

0 

Cosine  | 

Sine    |   |  Cotang. 

|    Tang. 

M. 

89  Degrees. 


SINES   AND    TANGENTS. 


M. 

Sine   |   D.   |  Cosine   |  D. 

Tang.      D.     Cotang. 

0 

8.241855 

11963 

9.999934 

04 

8.241921 

11967 

11.758079 

60 

1 

249033 

11768 

999932 

04 

249102 

11772 

750898 

59 

2 

256094 

11580 

999929 

04 

256165 

11584 

743835 

58 

3 

263042 

11398 

999927 

04 

263115 

11402 

736885 

57 

4 

269881 

11221 

999925 

04 

269956 

11225 

730044 

56 

5 

276614 

11050 

999922 

04 

276691 

11054 

723309 

55 

6 

283243 

10883 

999920 

04 

283323 

10887 

716677 

54 

7 

289773 

10721 

999918 

04 

289856 

10726 

710144 

53 

8 

296207 

10585 

999915 

04 

296292 

10570 

703708 

52 

9 

302546 

10413 

999913 

04 

302634 

10418 

697366 

51 

10 

308794 

10266 

999910 

04 

308884 

10270 

691116 

50 

11 

8.314954 

10122 

9.999907 

04 

8.315046 

10126 

11.684954 

49 

12 

321027 

9982 

999905 

04 

321122 

9987 

678878 

48 

13 

327016 

9847 

999902 

04 

327114 

9851 

672886 

47 

14 

332924 

9714 

999899 

05 

333025 

9719 

666975 

46 

15 

338753 

9586 

999897 

05 

338956  9590 

661144 

45 

16 

344504 

9460 

999894 

05 

344610  9465 

655390 

44 

17 

350181 

9338 

999891 

05 

350289 

9343 

649711 

43 

18 

355783 

9219 

999888 

05 

355895 

9224 

644105 

42 

19 

361315 

9103 

999885 

05 

361430 

9108 

638570 

41 

20 

366777 

8990 

999882 

05 

366895 

8995 

633105 

40 

21 

8.372171 

8880 

9.999879 

05 

8.372292 

8885 

11.627708 

39 

22 

377499 

8772 

999876 

05 

377622 

8777 

622378 

38 

23 

382762 

8667 

999873 

05 

382889 

8672 

617111 

37 

24 

387962 

8564 

999870 

05 

388092 

8570 

611908 

36 

25 

393101 

8464 

999S67 

05 

393234 

8470 

606766 

35 

26 

398179 

8366 

999864 

05 

398315 

8371 

601685 

34 

27 

403199 

8271 

999861 

05 

403338 

8276 

596662 

33 

28 

408161 

8177 

999858 

05 

408304 

8182 

591696 

32 

29 

413068 

8086 

999854 

05 

413213 

8091 

586787 

31 

30 

417919 

7996 

999851 

00 

418068 

8002 

581932 

30 

31 

8.422717 

7909 

9.999848 

06 

8.422869 

7914 

11.577131 

29 

32 

427462 

7823 

999844 

OfJ 

427618 

7830 

572382 

28 

33 

432156 

7740 

999841 

06 

432315 

7745 

567685 

27 

34 

436800 

7657 

999838 

00 

436962 

7663 

563038 

26 

35 

441394 

7577 

999834 

06 

441560 

7583 

558440 

25 

36 

445941 

7499 

999831 

06 

446110 

7505 

553890 

24 

37 

450440 

7422 

999827 

06 

450613 

7428 

549387 

23 

38 

454893 

7346 

999823 

06 

455070 

7352 

544930 

22 

39 

459301 

7273 

99982C 

<>f> 

459481 

7279 

540519 

21 

40 

463665 

7200 

999816 

Of5 

463849 

7206 

536151 

20 

41 

8.467985 

7129 

9.999812 

or, 

8.468172 

7135 

11.531828 

19 

42 

472263 

7060 

999809 

06 

472454 

7066 

527546 

18 

43 

476498 

6991 

999805 

06 

476693J  6998 

523307 

17 

44 

480693 

6924 

99980  J 

06 

480892  6931 

519108 

16 

45 

484848 

6859 

999797 

07 

4S5050  6865 

514950 

15 

46 

488963 

6794 

999793 

07 

489170  '6801 

510830 

14 

47 

493040 

6731 

999790 

07 

493250  6738 

506750 

13 

48 

497078 

6669 

999788 

07 

497293 

6676 

502707 

12 

49 

501080 

6608 

999782 

07 

501298 

6615 

498702 

11 

50 

505045 

6548 

999778 

07 

505267 

6555 

494733 

10 

51 

8.508974 

6489 

9.999774 

07 

8.509200 

6496 

11.490800 

£ 

52 

512867 

6431 

999769 

07 

513098 

6439 

486902 

8 

53 

516726 

6375 

999765 

07 

516961 

6382 

483039 

"3 

54 

520551 

6319 

999761 

07 

5207PU 

6326 

479210 

6 

55 

52434? 

6264 

999757 

07 

5245k  5 

6272 

475414 

5 

56 

528102 

6211 

999753 

07 

528349 

6218 

471651 

4 

57 

531828 

6158 

999748 

07 

532080 

6165 

467920 

3 

58 

535523 

6106 

999744 

07 

535779 

6113 

464221 

2 

59 

53918fj 

6055 

999740 

07 

639447 

6062 

460553 

1 

60 

542819 

6004  1   999735  07l   543084 

6012 

456910 

0 

Cosine  1 

Sine   | 

Cotang.  | 

Tang    |AJ. 

c&  Degrees 


so 


(2  Degrees. )     A  TABLE  OF  LOGARITHMIC 


M.|   Sine   |   D. 

Cosine   \  D.  |   Tang.      D. 

Cotang.   | 

0 

8.542819 

6004 

9.999735 

07 

8.543084 

6012 

11.456916 

60 

1 

546422 

5955 

999731 

07 

546691 

5962 

453309 

59 

2 

549995 

5906 

999726 

07 

550268 

5914 

449732 

58 

3 

553539 

5858 

999722 

08 

553817 

5866 

446183 

57 

4 

557054 

5811 

999717 

08 

557336 

5819 

442664 

56 

6 

560540 

5765 

999713 

08 

560828 

5773 

439172 

55 

6 

563999 

5719 

999708 

08 

564291 

5727 

435709 

54 

7 

567431 

5674 

999704 

08 

567727 

5682 

432273 

53 

8 

570836 

5630 

999699 

08 

571137 

5638 

428863 

52 

9 

574214 

5587 

999694 

08 

574520 

5595 

425480 

51 

10 

577566 

5544 

999689 

08 

577877 

5552 

422123 

50 

11 

8.580892 

5502 

9.999685 

08 

8.581208 

5510 

11.418792 

49 

12 

584193 

5460 

999680 

08 

584514 

5468 

415486 

48 

13 

587469 

5419 

999675 

08 

587795 

5427 

412205 

47 

14 

590721 

5379 

999670 

08 

591051 

5387 

408949 

46 

15 

593948 

5339 

999665 

08 

594283 

5347 

405717 

45 

16 

597152 

5300 

999660 

08 

597492 

5308 

402508 

44 

17 

600332 

5261 

999655 

08 

600677 

5270 

399323 

43 

18 

603489 

5223 

999650 

08 

603839 

5232 

396161 

42 

19 

606623 

5186 

999645 

09 

606978 

5194 

393022 

41 

20 

609734 

5149 

999640 

09 

610094 

5158 

389906 

40 

21 

8.612823 

5112 

9.999635 

09 

8.613189 

5121 

11.386811 

39 

22 

615891 

5076 

999629 

09 

616262 

5085 

383738 

38 

23 

618937 

5041 

999624 

09 

619313 

5050 

380687 

37 

24 

621962 

5006 

999619 

09 

622343 

5015 

377657 

36 

25 

624965 

4972 

999614 

09 

625352 

4981 

374648 

35 

26 

627948 

4938 

999608 

09 

628340 

4947 

371660 

34 

27 

630911 

4904 

999603 

09 

631308 

4913 

368692 

33 

28 

633854 

4871 

999597 

09 

634256 

4880 

365744 

32 

29 

636776 

4839 

999592 

09 

637184 

4848 

362816 

31 

30 

639680 

4806 

999586 

09 

640093 

4816 

359907 

30 

31 

8.642563 

4775 

9.999581 

09 

8.642982 

4784 

11.357018 

29 

32 

645428 

4743 

999575 

09 

645853 

4753 

354147 

28 

33 

648274 

4712 

999570 

09 

648704 

4722 

351296 

27 

34 

651102 

4682 

999564 

09 

651537 

4691 

348463 

26 

35 

653911 

4652 

999558 

10 

654352 

4661 

345648 

25 

36 

656702 

4622 

999553 

10 

657149 

4631 

342851 

24 

37 

659475 

4592 

999547 

10 

659928 

4602 

340072 

23 

38 

662230 

4563 

999541 

10 

662689 

4573 

337311 

22 

39 

664968 

4535 

999535 

10 

665433 

4544 

334567 

21 

40 

667689 

4506 

999529 

10 

668160 

4526 

331840 

20 

41 

8.670393 

4479 

9.999524 

10 

8.670870 

4488 

11.329130 

19 

42 

673080 

4451 

999518 

10 

673563 

4461 

326437 

18 

43 

675751 

4424 

999512 

10 

676239 

4434 

323761 

17 

44 

678405 

4397 

999506 

10 

678900 

4417 

321100 

16 

45 

681043 

4370 

999500 

10 

681544 

4380 

318456 

15 

46 

683665 

4344 

999493 

10 

684172 

4354 

315828 

14 

47 

686272 

4318 

999487 

10 

686784 

4328 

313216 

13 

48 

688863 

4292 

999481 

10 

689381 

4303 

310619 

12 

49 

691438 

4267 

999475 

10 

691963 

4277 

308037 

11 

50 

693998 

4242 

999469 

10 

694529 

4252 

305471 

10 

51 

8.696543 

4217 

9.999463 

11 

8.697081 

4228 

11.302919 

9 

52 

699073 

4192 

999456 

11 

699617 

4203 

300383 

8 

53 

701589 

4168 

999450 

11 

702139 

4179 

297861 

7 

54 

704090 

4144 

999443 

11 

704646 

4155 

295354 

6 

55 

706577 

4121 

999437 

11 

707140 

4132 

292860 

5 

56 

709049 

4097 

999431 

11 

709618 

4108 

290382 

4 

57 

711507 

4074 

999424 

11 

712083 

4085 

287917 

3 

58 

713952 

4051 

999418 

11 

714534 

4062 

285465 

2 

59 

716383 

4029 

999411 

11 

716972 

4040 

283028 

1 

60 

718800 

4006 

999404 

11 

719396 

4017 

280604 

0 

Cosine   1          Sine 

Cotanc. 

Tang.    |M. 

87  Degree*. 


SINES  AND  TANGENTS.     (3  Degrees.) 


21 


M.  |   Sine   j   D. 

Cosine   D.    Tan?.      D.   |  Cotanir.   | 

0 

8.718800 

4006 

9  .  999404 

11 

8.719396)  4017 

11.280604 

60 

1 

721204 

3984 

999398 

11 

721806  3995 

278194 

59 

2 

723595 

3962 

999391 

11 

724204 

3974 

275796 

58 

3 

725972 

3941 

999384 

11 

726588 

3952 

273412 

57 

4 

728337 

3919 

999378 

11 

728959 

3930 

271041 

56 

5 

730688 

3898 

999371 

11 

731317 

3909 

268683 

55 

6 

733027 

3877 

999364 

12 

733663 

3889 

266337 

54 

7 

735354 

3857 

999357 

12 

735996 

3868 

264004 

53 

8 

737607 

3836 

999350 

12 

738317 

3848 

261683 

52 

9 

739969 

3816 

999343 

12 

740626 

3827 

259374 

51 

10 

742259 

3796 

999336 

12 

742922 

3807 

257078 

50 

11 

8.744536 

3776 

9.999329 

12 

8.745207 

3787 

11.254793 

49 

12 

746802 

3756 

999322 

12 

747479 

3768 

252521 

48 

13 

749055 

3737 

999315 

12 

749740 

3749 

250260 

47 

14 

751297 

3717 

999308 

12 

751989 

3729 

248011 

46 

15 

753528 

3698 

999301 

12 

754227 

3710 

245773 

45 

16 

755747 

3679 

999294 

12 

756453 

3692 

243547 

44 

17 

757955 

3661 

999286 

12 

758668 

3673 

241332 

43 

18 

760151 

3642 

999279 

12 

760872 

3655 

239128 

42 

19 

762337 

3624 

999272 

12 

763065 

3636 

236935 

41 

20 

764511 

3606 

999265 

12 

765246 

3618 

234754 

40 

21 

8.766675 

3588 

9.999257 

12 

8.767417 

3600 

11.232583 

39 

22 

768828 

3570 

999250 

13 

769578 

3583 

230422 

38 

23 

770970 

3553 

999242 

13 

771727 

3565 

228273 

37 

24 

773101 

3535 

999235 

13 

773866 

3548 

226134 

36 

25 

775223 

3518 

999227 

13 

775995 

3531 

224005 

35 

26 

777333 

3501 

999220 

13 

778114 

3514 

221886 

34 

27 

779434 

3484 

999212 

13 

780222 

3497 

219778 

33 

28 

781524 

3467 

999205 

13 

782320 

3480 

217680 

32 

29 

783605 

3451 

999197 

13 

784408 

3464 

215592 

31 

30 

785675 

3431 

999189 

13 

786486 

3447 

213514 

30 

31 

8.787736 

3418 

9.999181 

13 

8  .  788554 

3431 

11.211446 

29 

32 

789787 

3402 

999174 

13 

790613 

3414 

209387 

28 

33 

791828 

3386 

999166 

13 

792662 

3399 

207338 

27 

34 

793859 

3370 

999158 

13 

794701 

3383 

205299 

26 

35 

795881 

3354 

999150 

13 

796731 

3368 

203269 

25 

36 

797894 

3339 

999142 

13 

798752 

3352 

201248 

24 

37 

799897 

3323 

999134 

13 

800763 

3337 

199237 

23 

38 

801892 

3308 

999126 

13 

802765 

3322 

197235 

22 

39 

803876 

3293 

999118 

13 

804758 

3307 

195242 

21 

40 

805852 

3278 

999110 

13 

806742 

3292 

193258 

20 

41 

8.807819 

3263 

9.999102 

13 

8.808717 

3278 

11.191283 

19 

42 

809777 

3249 

999094 

14 

810683 

3262 

189317 

18 

43 

811726 

3234 

999086 

14 

81^2641 

3248 

187359 

17 

44 

813667 

3219 

999077 

14 

814589 

3233 

185411 

16 

45 

815599 

3205 

999069 

14 

816529 

3219 

183471 

15 

46 

817522 

3191 

999061 

14 

818461 

3205 

181539 

14 

47 

819436 

3177 

999053 

14 

820384 

3191 

179616 

13 

48 

821343 

3163 

999044 

14 

822298 

3177 

177702 

12 

49 

823240 

3149 

999036 

14 

824205 

3163 

175795 

11 

50 

825130 

3135 

999027 

14 

826103 

3150 

173897 

10 

51 

8.827011 

3122 

9.999019 

14 

8.827992 

3136 

11.172008 

9 

52 

828884 

3108 

999010 

14 

829874 

3123 

170126 

8 

53 

830749 

3095 

999002 

14 

831748 

3110 

168252 

7 

54 

832607 

3082 

998993 

14 

833613 

3096 

166387 

6 

55 

834456 

3069 

998984 

14 

835471 

3083 

164529 

5 

56 

836297 

3056 

998976 

14 

837321 

3070 

162679 

4 

57 

838130 

3043 

998967 

15 

839163 

3057 

160837 

3 

58 

839956 

3030 

998958 

15 

840998 

3045 

159002 

2 

59 

841774 

3017 

998950 

15 

842825 

3032 

157175 

1 

60 

843585 

3000 

998941 

15 

844644 

3019 

155356 

0 

Cosine 

Sine   j     Cotang.            Tang.    |  M. 

86  Degrees. 


(4  Degrees.)     A  TABLE  or  LOGARITHMIC 


M.    Sine   |   D.     Cosine    D.    Tang.     D.   |   Cotang.  | 

0 

8.843585 

3005 

9.998941 

Jb 

8  .  844644 

3019 

11.155356 

60 

1 

845387 

2992 

998932 

15 

846455 

3007 

153545 

59 

2 

847183 

2980 

998923 

15 

848260 

2995 

151740 

58 

3 

848971 

2P67 

998914 

15 

850057 

2982 

149943 

57 

4 

850751 

2955 

998905 

15 

851846 

2970 

148154 

56 

5 

852525 

2943 

998896 

15 

853628 

2958 

146372 

55 

6 

854291 

2931 

998887 

15 

855403 

2946 

144597 

54 

7 

856049 

2919 

998878 

15 

857171 

2935 

142829 

53 

8 

857801 

2907 

998869 

15 

858932 

2923 

141068 

52 

9 

859546  2896 

998860 

15 

860686 

2911 

139314 

51 

10 

861283!  2884 

998851!  15 

862433 

2900 

137567 

50 

11 

8.863014  2873 

9.998841 

15 

8.864173 

2888 

11.135827 

49 

12 

864738 

2861 

998832 

15 

865906 

2877 

134094 

48 

13 

866455 

2850 

998823 

16 

867632 

2866 

132368 

47 

14 

868165 

2839 

998813 

16 

869351 

2854 

1  30649 

46 

15 

869868 

2828 

998804 

16 

871064 

2843 

128936 

45 

16 

871565 

2817 

998795 

16 

872770 

2832 

127230 

44 

17 

873255 

2806 

998785 

16 

874469 

2821 

125531 

43 

18 

874938 

2795 

998776 

16 

876162 

2811 

123838 

42 

19 

876615 

2786 

998766 

16 

877849 

2800 

122151 

41 

20 

878285 

2773 

998757 

16 

879529 

2789 

120471 

40 

21 

8.879949 

2763 

9.998747 

16 

8.881202 

2779 

11.118798 

39 

22 

881607 

2752 

998738 

16 

882869 

2768 

117131 

38 

23 

883258 

2742 

998728 

16 

884530 

2758 

115470 

37 

24 

884903 

2731 

998718 

16 

886185 

2747 

113815 

36 

25 

886542 

2721 

998708 

16 

887833 

2737 

112167 

35 

26 

888174 

2711 

998699 

16 

889476 

2727 

110524 

34 

27 

889801 

2700 

998689 

16 

891112 

2717 

108888 

33 

28 

891421 

2690 

998679 

16 

892742 

2707 

107258 

32 

29 

893035 

2680 

998669 

17 

894366 

2697 

105634 

31 

30 

894643 

2670 

998659 

17 

895984 

2687 

104016 

30 

31 

8.896246 

2660 

9.998649 

17 

8.897596 

2677 

11.102404 

29 

32 

897842 

2651 

998639 

17 

899203 

2667 

100797 

28 

33 

899432 

2641 

998629 

17 

900803 

2658 

099197 

27 

34 

901017 

2631 

998619 

17 

902398 

2648 

097602 

26 

35 

902596 

2622 

998609 

17 

903987 

2638 

096013 

25 

36 

904169 

2612 

998599 

17 

905570 

2629 

094430 

24 

37 

905736 

2603 

998589 

17 

907147 

2620 

092853 

23 

38 

907297 

2593 

998578 

17 

908719 

2610 

091281 

22 

39 

908853 

2584 

998568 

17 

910285 

2601 

089715 

21 

40 

910404 

2575 

998558 

17 

911846 

2592 

.  088154 

20 

41 

8.911949 

2566 

9.998548 

17 

8.913401 

2583 

11.086599 

19 

42 

913488 

2556 

998537 

17 

914951 

2574 

085049 

18 

43 

915022 

2547 

998527 

17 

916495 

2565 

083505 

17 

44 

916550 

2538 

998516 

18 

918034 

2556 

081966 

16 

45 

918073 

2529 

998506 

18 

919568 

2547 

080432 

15 

46 

919591 

2520 

998495 

18 

921096 

2538 

078904 

14 

47 

921103 

2512 

998485 

18 

922619 

2530 

077381 

13 

48 

922610 

2503 

998474 

18 

924136 

2521 

075864 

12 

49 

924112 

2494 

998464 

18 

925649 

2512 

074351 

11 

50 

925609 

2486 

998453 

18 

927156 

2503 

072844 

10 

51 

8.927100 

2477 

9.998442 

18 

8.928658 

2495 

11.071342 

9 

52 

928587 

2469 

998431 

18 

930155 

2486 

069845 

8 

53 

930068 

2460 

998421 

18 

931647 

2478 

068353 

7 

54 

931544 

2452 

998410 

18 

933134 

2470 

066866 

6 

55 

933015 

2443 

998399 

18 

934616 

2461 

065384 

5 

56 

934481 

2435 

998388 

18 

936093 

2453 

U63907 

4 

57 

935942 

2427 

998377 

18 

937565 

2445 

062435 

3 

58 

937398 

2419 

998366 

18 

939032 

2437 

060968 

2 

59 

938850 

2411 

998355 

18 

940494 

2430 

059506 

1 

60 

940296 

2403 

998344 

18 

941952 

2421 

058048 

0 

Cosine 

Sine 

Cotang. 

|   Tang. 

ML 

85  Degrees. 


BINES  AND  TANGENTS.     ^5  Degrees.) 


|  M.  |   Sine   |   D. 

Cosine    D.  j   Tang. 

D.   |  Ootang.   | 

0 

8.940296 

2403 

9.998344 

19 

8.941952 

2421 

11.058048 

60 

1 

941738 

2394 

998333 

19 

943404 

2413 

056596 

59 

2 

943174 

2387 

998322 

19 

944S52 

2405 

055148 

58 

3 

944606 

2379 

998311 

19 

946295 

2397 

053705 

57 

4 

946034 

2371 

998300 

19 

947734 

2390 

052266 

56 

6 

947456 

2363 

998289 

19 

949168 

2382 

050832 

55 

p 

948874 

2355 

998277 

19 

950597 

2374 

049403!  54 

V 

950287 

2348 

998266 

19 

952021 

2366 

047979  53 

8 

951696 

2340 

998255 

19 

953441 

2360 

0465591  52 

!• 

953100 

2332 

998243 

19 

954856 

2351 

045144 

51 

10 

954499 

2325 

998232 

19 

956267 

2344 

043733 

50 

11 

8  .  955894 

2317 

9.998220 

19 

8.957674 

2337 

11.042326 

49 

n 

957284 

2310 

998209 

19 

959075 

2329 

040925 

48 

11 

958670 

2302 

998197 

19 

960473 

2323 

039527 

47 

14 

960052 

2295 

998186 

19 

961866 

2314 

038134 

46 

IA 

961429 

2288 

998174 

19 

963255 

2307 

036745 

45 

16 

962801 

2280 

998163 

19 

964639 

2300 

035361 

44 

17 

964170 

2273 

998151 

19 

966019 

2293 

033981 

43 

18 

965534 

2266 

998139 

20 

9673941  2286 

032606 

42 

19 

966893 

2259 

998128 

20 

968766 

2279 

031234 

41 

20 

96S249 

2252 

998116 

20 

970133 

2271 

029867 

40 

21 

8.969600 

2244 

9.998104 

20 

8.971496 

2265 

1  1  .  028504 

39 

22 

970947 

2238 

998092 

20 

972855 

2257 

027145 

38 

23 

972289 

2231 

998080 

20 

974209 

2251 

025791 

37 

24 

973628 

2224 

998068 

20 

975560 

2244 

024440 

36 

25 

974962 

2217 

998056 

20 

976906 

2237 

023094 

35 

26 

976293 

2210 

998044 

20 

978248 

2230 

021752 

34 

27 

977619 

2203 

998032 

20 

979586 

2223 

020414 

33 

28 

978941 

2197 

998020 

20 

930921 

2217 

019079 

32 

29 

980259 

2190 

998008 

20 

982251 

2210 

017749 

31 

30 

931573 

2183 

997996 

20 

983577 

2204 

0164231  30 

31 

8.982883 

2177 

9.997984 

20 

8.984899 

2197 

11.015101 

29 

32 

984189 

2170 

997972 

20 

986217 

2191 

013783 

28 

33 

98549  1 

2163 

997959 

20 

987532 

2184 

012468 

27 

34 

986789 

2157 

997947 

20 

988842 

2178 

011158 

26 

35 

988083 

2150 

997935 

21 

990149 

2171 

009851 

25 

36 

989374 

2144 

997922 

21 

991451 

2165 

008549 

24 

37 

990660 

2138 

997910 

21 

992750 

2158 

007250 

23 

38 

991943 

2131 

997897 

21 

994045 

2152 

005955 

22 

39 

993222 

2125 

997885 

21 

995337 

2146 

004663 

21 

40 

934497 

2119 

997872 

21 

996624 

2140 

003376 

20 

41 

8.995768 

2112 

9.997860 

21 

8  .  997908 

2134 

11.002092 

19 

42 

997036 

2106 

997847 

21 

999188 

2127 

000812 

18 

43 

998299 

2100 

997835 

21 

9.000465 

2121 

10.999535 

17 

44 

999560 

2094 

997822 

21 

001738 

2115 

998262 

16 

45 

9.000816 

2087 

997809 

21 

003007 

2109 

996993 

15 

46 

002069 

2082 

997797 

21 

004272 

2103 

995728 

14 

47 

003318 

2076 

997784 

21 

005534 

2097 

994406 

13 

48 

004563 

2070 

997771 

21 

006792 

2091 

993208 

12 

49 

005805 

2064 

997758 

21 

008047 

2085 

991953 

11 

50 

007044 

2058 

997745 

21 

009298 

2080 

990702 

0 

51 

9.008278  2052 

9.997732 

21 

9.010546 

2074 

10.989454 

9 

52 

009510  2046 

997719 

21 

011790 

2068 

988210 

8 

53 

010737  2040 

997706 

21 

013031 

2062 

986969 

7 

54 

0119621  2034 

997693 

22 

014268 

2056 

985732 

6 

55 

013182;  2029 

997680 

22 

015502 

2051 

984498 

5 

56 

014400  2023 

997667!  22 

Olb/32 

2045 

983268 

4 

57 

015613  2017 

997654  22 

017959 

2040 

982041 

3 

58 

016824!  2012 

997641  22 

019183 

2033 

980817 

2 

59 

0180311  2006 

997628;  22 

020403 

2028 

979597 

1 

60 

019235  2000 

997614122 

021620 

2023 

978380 

0 

|  Cosine  j         Sine 

Cotang.   | 

Tang.   |  M. 

84  Degrees. 


2*4 


(6  Degrees.)      A  TABLE  OF  LOGARITHMIC 


M 

Sine   | 

D. 

Cosine   |  D. 

Tang      D. 

Cotang. 

0 

9.019235 

2000 

9.997614 

22 

9.021620  2023 

0.978380 

60 

1 

020435 

1995 

997601 

22 

022834J  2017 

977166 

59 

2 

021632 

1989 

997588 

22 

024044  2011 

975956 

58 

3 

022825 

1984 

997574 

22 

025251  2006 

974749 

57 

4 

024016 

1978 

997561 

22 

026455!  2000 

973545 

56 

5 

025203 

1973 

997547 

22 

0276551  1995 

972345 

55 

6 

026386 

1967 

997534 

23 

028852  1990 

971148 

54 

7 

027567 

1962 

997520 

23 

030046 

1985 

969954 

53 

8 

028744 

1957 

997507 

23 

031237 

1979 

968763 

52 

9 

029918 

1951 

997493 

23 

032425 

1974 

?67575 

51 

10 

031089 

1947 

997480 

23 

033609  1969 

966391 

50 

11 

9.032257 

1941 

9.997466 

23 

9.034791   1964 

0.965209 

49 

12 

033421 

1936 

997452 

23 

035969!  1958 

964031 

48 

13 

034582 

1930 

997439 

23 

0371441  1953 

962856 

47 

14 

035741 

1925 

997425 

23 

038316  1948 

961684 

46 

15 

036896 

1920 

997411 

23 

0394851  1943 

960515 

45 

16 

038048 

1915 

997397 

23 

04065  l!  1938 

959349 

44 

17 

039197 

1910 

997383 

23 

041813  1933 

958187 

43 

18 

040342 

1905 

997369 

23 

042973  1928 

957027 

42 

19 

041485 

1899 

997355 

23 

044130  1923 

955870 

41 

20 

042625 

1894 

997341 

23 

045284J  1918 

954716 

40 

21 

9.043762 

1889 

9.997327 

24 

9.046434!  1913 

10.953566 

39 

22 

044895 

1884 

997313 

24 

047582 

1908 

952418 

38 

23 

046026 

1879 

997299 

24 

048727 

1903 

951273 

37 

24 

047154 

1875 

997285 

24 

049869 

1898 

950131 

36 

25 

048279 

1870 

997271 

24 

051008!  1893 

948992 

35 

26 

049400 

1865 

997257 

24 

052144  1889 

947856 

34 

27 

050519 

1860 

997242 

24 

053277 

1884 

946723 

33 

28 

051635 

1855 

997228 

24 

054407  1879 

945593 

32 

29 

052749 

1850 

997214 

24 

055535 

1874 

944465 

31 

30 

053859 

1845 

997199 

24 

056659  1870 

943341 

30 

31 

054966 

1841 

9.997185 

24 

9.057781   1865 

10.942219 

29 

32 

056071 

1836 

997170 

24 

058900'  1869 

941100 

28 

33 

057172 

1831 

997156 

24 

060016!  1855 

939984 

27 

34 

058271 

1827 

997141 

24 

061130!  1851 

938870 

26 

35 

059307 

1822 

997127 

24 

062240:  1846 

937760 

25 

36 

060460 

1817 

997112 

24 

063348:  1842 

936652 

24 

37 

061551 

1813 

9117098 

24 

064453  1837 

935547 

23 

38 

062639 

1808 

997083 

25 

065556J  1833 

934444 

22 

39 

063724 

1804 

997068 

25 

066655  1828 

933345 

21 

40 

064806 

1799 

997053 

25 

067752 

1824 

932248 

20 

41 

9.0658S5 

1794 

9  .  997039 

'25 

9.068846J  1819 

10.931154 

19 

42 

066962 

1790 

997024 

25 

069938!  1815 

930062 

18 

43 

068036 

1786 

997009 

25 

071027  1810 

928973 

17 

44 

069107 

1781 

996994 

25 

0721131  1806 

927887 

16 

45 

070176 

1777 

996979 

25 

073197  1802 

926803 

15 

46 

071242 

1772 

996964 

25 

074278 

1797 

925722 

14 

47 

072306 

1768    996949 

25 

075356 

1793 

924644 

13 

48 

073366 

1763 

996934 

25 

076432 

1789 

923568 

12 

49 

074424 

1759 

996919 

25 

077505 

1784 

922495 

11 

50 

075480 

1755 

996904 

25 

078576 

1780 

921424 

10 

51 

9.076533 

1750 

9.996889 

25 

9.079644 

1776 

10.920356 

9 

52 

077583 

:  1746 

996874 

25 

080710 

1772 

919290 

8 

53 

078631 

:  1742 

996858 

25 

081773 

1767 

918227 

7 

64 

079676 

1738 

996843 

25 

082833 

1763 

917167 

6 

55 

080719 

1733 

996828 

25 

083891 

1759 

916109 

5 

56 

081759 

1729 

996812 

26 

084947J  1755 

915053 

4 

57 

08279V 

!  1725 

996797 

26 

0860001  1751 

914000 

J 

58 

083832 

1721 

996782 

26 

0870501  1747 

912950 

2 

69 

084864 

1717 

996766 

26 

088098 

1743 

911902 

1 

60 

085894 

1713    996751 

26 

089144 

1738 

910856 

0 

|  Cosine  | 

Sine    | 

(In  ang. 

Tang. 

M. 

83  Degreed. 


SINES  AND  TANGENTS.     ^7  Degrees.) 


25 


M.  1   Sine      D.   |  Cosine   |  D.  )   Tang.   |   D.     Cotang.   | 

0 

9.085894 

1713 

9.996751 

2b 

9.089144 

1738 

10.910850 

60 

1 

086922 

1709 

996735 

26 

090187 

1734 

909813 

59 

2 

087947 

1704 

996720  26 

091228 

1730 

908772 

58 

3 

088970 

1700 

996704 

26 

092266 

1727 

907734 

57 

4 

089990 

1696 

996688 

26 

093302 

1722 

906698 

56 

5 

091008 

1692 

996673 

26 

094336 

1719 

905664 

55 

6 

092024 

1688 

996657 

26 

095367 

1715 

904603  54 

7 

093037 

1684 

996641 

26 

096395 

1711 

903605 

53 

8 

094047 

1680 

996625 

26 

097422 

1707 

902578 

52 

9 

095056 

1676 

996610 

26 

098446 

1703 

901554 

5\ 

10 

09G062 

1673 

996594 

26 

099468 

169:) 

S  00532 

50 

11 

9.097065)  1668 

9.996578 

27 

9.100487 

1695 

10.899513 

49 

12 

098066 

1665 

996562 

27 

101504 

1691 

898496 

48 

13 

099065 

1661 

996546 

27 

102519 

1687 

897481 

47 

14 

100062 

1657 

996530 

27 

103532 

1684 

896468 

46 

15 

101056 

1653 

996514 

27 

104542 

1680 

895458 

45 

16 

102048 

1649 

996498 

27 

105550 

1676 

894450 

44 

17 

103037 

1645 

996482 

27 

106556 

1672 

893444 

43 

18 

104025 

1641 

996465 

27 

107559 

1669 

892441 

42 

19 

105010 

1638 

996449 

27 

108560 

1665 

891440 

41 

20 

105992 

1634 

996433 

27 

109559 

1661 

890441 

40 

21 

9.106973 

1630 

9.996417 

27 

9.110556 

1658 

10.889444 

39 

22 

107951 

1627 

996400 

27 

111551 

1654 

888449 

38 

23 

108927 

1623 

996384 

27 

112543 

1650 

887457 

37 

24 

109901 

1619 

996368 

27 

113533 

1646 

886467 

36 

25 

110873 

1616 

996351 

27 

114521 

1643 

885479 

35 

26 

111842 

1612 

996335 

27 

115507 

1639 

884493 

34 

27 

112809 

1608 

990318 

27 

116491 

1636 

883509 

33 

28 

1  13774 

1605 

996302 

28 

117472 

1632 

882528 

32 

29 

114737 

1601 

996285 

28 

118452 

1629 

881548 

31 

30 

1  15698 

1597 

996269 

28 

119429 

1625 

880571 

30 

31 

9.116656 

1594 

9.996252 

28 

9.120404 

1622 

10.879596 

29 

32 

117613 

1590 

996235 

28 

121377 

1618 

878623 

28 

33 

118567 

1587 

996219 

28 

122348 

1615 

877652 

27 

34 

119519 

1583 

996202 

28 

123317 

1611 

876683 

26 

35 

120469 

1580 

996185 

28 

124284 

1607 

875716 

25 

36 

121417 

1576 

996168 

28 

125249 

1604 

874751 

24 

37 

122362 

1573 

996151 

28 

126211 

1601 

873789 

23 

38 

123306 

1569 

996134 

28 

127172 

1597 

872828 

22 

39 

124248 

1566 

996117 

28 

128130 

1594 

871870 

21 

40 

125187 

1562 

996100 

28 

129087 

1591 

870913 

20 

41 

9.126125 

1559 

9.996083 

29 

9.130041 

1587 

10.869959 

19 

42 

127060 

1556 

996066 

29 

130994 

1584 

869006 

18 

43 

127993 

1552 

996049 

29 

131944 

1581 

868056 

17 

44 

128925 

1549 

996032 

29 

132893 

1577 

867107 

16 

45 

129854 

1545 

996015 

29 

133839 

1574 

866161 

15 

46 

130781 

1542 

995998 

29 

134784 

1571 

865216 

14 

47 

131706 

1539 

995980 

29 

135726 

1567 

864274 

13 

48 

132630 

1535 

995963 

29 

136667 

1564 

863333 

12 

49 

133551 

1532 

995946 

29 

137605 

1561 

862395 

11 

50 

134470 

1529 

995928 

29 

138542 

1558 

861458 

10 

51 

9.135387 

1525 

9.995911 

29 

9.139476 

1555 

10.860524 

9 

52 

136303 

1522 

995894 

29 

140409 

1551 

859591 

8 

53 

137216 

1519 

995876 

29 

141340 

1548 

858660 

7 

54 

138128 

1516 

995859 

29 

142269 

1545 

857731 

6 

55 

139037 

1512 

995841 

29 

143196 

1542 

856804 

5 

56 

139944 

1509 

995823  29 

144121 

1539 

855879 

4 

57 

140850 

1506 

995806  29 

145044 

1535 

854956 

3 

58 

141754 

1503 

995788  29 

145966 

1532 

854034 

2 

59 

142655t  1500 

995771 

29 

146885 

1529 

853115 

1 

60 

1435551  1496 

995753 

29 

147803'  15216 

852197 

0 

|  Cosine  j 

Sine   |      (  oiaiis.  |          Tung    M. 

82  Degrees. 


(8  Degrees.;     A  TABLE  OP  LOGARITHMIC 


M.    Sine   |   D.   |   Conine    D.    Tang.     D.     Cutaiig. 

0 

9.143555 

1496 

9  .  995753 

30  9.147803 

1526 

10.852197  60 

1 

144453 

1493 

995735 

30    148718 

1523 

851282 

59 

2 

145349 

1490 

995717 

30  |   149632 

1520 

850368 

58 

3 

146243 

1487 

995699 

30    150544 

1517 

849456 

57 

4 

147136 

1484 

995681 

30 

151454 

1514 

848546 

56 

5 

148026 

1481 

995664 

30 

152363 

1511 

847637 

55 

6 

148915 

1478 

995646 

30 

153269 

1508 

846731 

54 

7 

149802 

1475 

995628 

30 

154174 

1505 

845826 

53 

8 

150686 

1472 

995610 

30 

155077 

1502 

844923 

52 

9 

151569 

1469 

995591 

30 

155978 

1499 

844022 

21 

10 

152451 

1466 

995573 

30 

156877 

1496 

843123 

50 

11 

9  153330 

1463 

9.995555 

30 

9.157775 

1493 

10.842225 

49 

12 

154208 

1460 

995537 

30 

158671 

1490 

841329 

48 

13 

155083 

1457 

995519 

30 

159565 

1487 

840435 

47 

14 

155957 

1454 

995501 

31 

160457 

1484 

839543 

46 

15 

156830 

1451 

995482 

31 

161347 

1481 

838653 

45 

16 

157700 

1448 

995464 

31 

162236 

1479 

837764 

44 

17 

158569 

1445 

995446 

31 

163123 

1476 

836877 

43 

18 

159435 

1442 

995427 

31 

164008 

1473 

835992 

42 

19 

160301 

1439 

995409 

31 

164892 

1470 

835108 

41 

20 

161164 

1436 

995390 

31 

165774 

1467 

834226 

40 

21 

9.162025 

1433 

9.995372 

31 

9.166654 

1464 

10.833346 

39 

22 

162885 

1430 

995353 

31 

167532 

1461 

832468 

38 

23 

1637431  1427 

995334  31 

168409 

1458 

831591 

37 

24 

164600 

1424 

995316 

31 

169284 

1455 

830716 

36 

25 

165454 

1422 

995297 

31 

170157 

1453 

829843 

35 

26 

166307 

1419 

995278 

31 

171029 

1450 

828971 

34 

27 

167159 

1416 

995260 

31 

171899 

1447 

828101 

33 

28 

168008 

1413 

995241 

32 

172767 

1444 

827233 

32 

29 

168856 

1410 

995222 

32 

173634 

1442 

826366 

31 

30 

169702 

1407 

995203 

32 

174499 

i439 

825501 

30 

31 

9.170547 

1405 

9.995184 

32 

9.175362 

1436 

10.824638 

29 

32 

171389 

1402 

995165 

32 

176224 

1433 

823776 

28 

33 

172230 

1399 

995146 

32 

177084 

1431 

822916 

27 

34 

173070 

1396 

995127 

32 

177942 

1428 

822058 

26 

35 

173908 

1394 

995108 

32 

178799 

.  1425 

821201 

25 

36 

174744 

1391 

995089 

32 

179655 

1423 

820345 

24 

37 

175578 

1388 

995070 

32 

180508 

1420 

819492 

23 

38 

176411 

1386 

995051 

32 

181360 

1417 

818640 

22 

39 

177242 

1383 

995032 

32 

182211 

1415 

817789 

21 

40 

178072 

1380 

995013 

32 

183059 

1412 

816941 

20 

41 

9.178900 

1377 

9.994993 

32 

9.183907 

1409 

10.816093 

19 

42 

179726 

1374 

994974 

32 

184752 

1407 

815248 

18 

43 

180551 

1372 

994955 

32 

185597 

1404 

814403 

17 

44 

181374 

1369 

994935 

32 

186439 

1402 

813561 

16 

45 

182196 

1366 

994916 

33 

187280 

1399 

812720 

15 

46 

183016 

1364 

994896 

33 

188120 

1396 

811880 

14 

47 

183834 

1361 

994877 

33 

188958 

1393 

811042 

13 

48 

184651 

1359 

994857 

33 

189794 

1391 

810206 

12 

49 

185466 

1356 

994838 

33 

190629 

1389 

809371 

11 

50 

186280 

1353 

994818 

33 

191462 

1386 

808538 

10 

51 

9.187092 

1351 

9.994798 

33 

9.192294 

1384 

10.807706 

9 

52 

187903 

1348 

994779 

33 

193124 

1381 

806876 

8 

53 

188712 

1346 

994759 

33 

193953 

1379 

806047 

7 

54 

189519 

1343 

994739 

33 

194780 

1376 

805220 

6 

55 

190325 

1341 

994719 

33 

195606 

1374 

804394 

5 

56 

191130 

1338 

994700 

33 

196430 

1371 

803570 

4 

57 

191933 

1336 

994680 

33 

197253 

1369 

802747 

3 

58 

192734 

1333 

994660 

33 

198074 

1366 

801926 

2 

59 

193534 

1330 

994640 

33 

198894 

1364 

801106 

7 

60 

194332 

1328 

994620 

33 

199713 

1361 

800287 

0 

Cosine   j       |   Sine 

Cutang. 

Tang. 

M. 

81  Degrees. 


SINES  AT<D  TANGKNTS.     (9  Degrees. ) 


27 


M.|   Sine   |   D. 

Cosine   |  D. 

Tang.   !   D 

Cotang. 

o 

9.194332 

1328 

9  .  994620 

1 

195129 

1326 

994600 

33 

200529 

1359 

799471 

59 

i 

195925 

1323 

994580 

33 

201345 

1356 

798655 

53 

196719 

1321 

994560 

34 

202159 

1354 

797841 

57 

4. 

197511 

1318 

994540 

34 

202971 

1352 

797029 

56 

ft 
5 

198302 

1316 

994519 

34 

203782 

1349 

796218 

55 

6 

199091 

1313 

994499 

34 

204592 

1347 

795408 

54 

7 

199879 

1311 

994479 

34 

205400 

1345 

794600 

53 

i 

g 

200666 

1308 

994459 

34 

206207 

1342 

793793 

52 

g 

201451 

1306 

994438 

34 

207013 

1340 

792987 

51 

10 

202234 

1304 

994418 

34 

207817 

1338 

792183 

50 

11 

9.203017 

1301 

9.994397 

34 

9.208619 

1335 

10.791381 

49 

12 

203797 

1299 

994377 

34 

209420 

1333 

790580 

48 

13 

204577 

1296 

994357 

34 

210220 

1331 

789780 

47 

14 

205354 

1294 

994336 

34 

211018 

1328 

788982 

46 

15 

206131 

1292 

994316 

34 

211815 

1326 

788185 

45 

16 

206906 

1289 

994295 

34 

212611 

1324 

787389 

44 

17 

207679 

1287 

994274 

35 

213405 

1321 

786595 

43 

18 

208452 

128* 

994254 

35 

214198 

1319 

785802 

42 

19 

209222 

1282 

994233 

35 

214989 

1317 

785011 

41 

20 

209992 

1280 

994212 

35 

215780 

1315 

784220 

40 

21 

9.210760 

1278 

9.994191 

35 

9.216568 

1312 

10.783432 

39 

22 

211526 

1275 

994171 

35 

217356 

1310 

782644 

38 

28 

212291 

1273 

994150 

35 

218142 

1308 

781858 

37 

24 

213055 

1271 

994129 

35 

218926 

1305 

781074 

36 

25 

213818 

1268 

994108 

35 

219710 

1303 

780290 

35 

26 

214579 

1266 

994087 

35 

220492 

1301 

779508 

34 

27 

215338 

1264 

994066 

35 

221272 

1299 

778728 

33 

28 

216097 

1261 

994045 

35 

222052 

1297 

777948 

32 

29 

216854 

1259 

994024 

35 

222830 

1294 

777170 

31 

30 

217609 

1257 

QQAoaa 

2o 

asoooo 

129-3 

TT6394 

30 

31 

9.218363 

1255 

97993981 

35 

9.224382 

1290 

10.775618 

29 

32 

219116 

1253 

993960 

35 

225156 

1288 

774844 

28 

33 

i-  219868 

1250 

993939 

35 

225929 

1286 

774071 

27 

34 

220618 

1248 

993918 

35 

226700 

1284 

773300 

26 

35 

221367 

1246 

993896 

36 

227471 

1281 

772529 

25 

36 

222115 

1244 

993875 

36 

228239 

1279 

771761 

24 

37 

222861 

1242 

993854 

36 

229007 

1277 

770993 

23 

38 

223606 

1239 

993832 

36 

229773 

1275 

770227 

22 

39 

224349 

1237 

993811 

36 

230539 

1273 

769461 

21 

40 

225092 

1235 

993789 

36 

231302 

1271 

768698 

20 

41 

9.225833 

1233 

9.993768 

36 

9.232065 

1269 

10.767935 

19 

42 

226573 

1231 

993746 

36 

232826 

1267 

.  767174 

18 

43 

227311 

1228 

993725 

36 

233586 

1265 

766414 

17 

44 

228048 

1226 

993703 

36 

234345 

1262 

765655 

16 

45 

228784 

1224 

993681 

36 

235103 

1260 

764897 

15 

46 

229518 

1222 

993660 

36 

235859 

1258 

764141 

14 

47 

230252 

1220 

993638 

36 

236614 

1256 

763386 

13 

48 

230984 

1218 

993616 

36 

237368 

1254 

762632 

12 

49 

231714 

1216 

993594 

37 

238120 

1252 

761880 

11 

50 

232444 

1214 

993572 

37 

238872 

1250 

761128 

10 

51 

9.233172 

1212 

9.993550 

37 

9.239622 

1248 

10.760378 

9 

52 

233899 

1209 

993528 

37 

240371 

1246 

759629 

8 

53 

234625 

1207 

993506 

37 

241118 

1244 

758882 

7 

54 

235349 

1205 

993484 

37 

241865 

1242 

758135 

6 

55 

236073 

1203 

993462 

37 

242610 

1240 

757390 

5 

56 

236795 

1201 

993440 

37 

243354 

1238 

756646 

4 

57 

237515 

1199 

993418 

37 

244097 

1236 

755903 

3 

58 

238235 

1197 

993396 

37 

244839 

1234 

755161 

o 

59 

238958 

1195 

993374 

37 

245579 

1232 

754421 

1 

60 

239670 

1193 

993351 

37 

246319 

1230 

753681 

0 

|  Cosine   ,         Sine   | 

Cutang. 

Tang.   |  M. 

80  Degrees. 


(10  Degrees.)     A  TABLE  OF  LOGARITHMIC 


M. 

Sine 

1   D. 

Cosine 

ID. 

|   Tang. 

1   D. 

Cotang. 

1 

9.24631S 

1230 

10.753681 

60 

1 

240386 

1191 

993329 

37 

24705? 

1228 

752943 

59 

2 

241101 

1189 

993307 

37 

247794 

1226 

752206 

5£ 

3 

241814 

1187 

993285 

37 

248530 

1224 

751470 

57 

4 

242526 

1185 

993262 

37 

249264 

1222 

750736 

56 

5 

243237 

1183 

993240 

37 

249998 

1220 

750002 

55 

6 

243947 

1181 

993217 

38 

250730 

1218 

749270 

54 

7 

244656 

1179 

993195 

38 

251461 

1217 

748539 

5c 

8 

245363 

1177 

993172 

38 

252191 

1215 

747809 

52 

9 

246069 

1175 

993149 

38 

252920 

1213 

747080 

51 

10 

246775 

1173 

993127 

38 

253648 

1211 

746352 

50 

11 

9.247478 

1171 

9.993104 

38 

9.254374 

1209 

10.745626 

49 

12 

248181 

1169 

993081 

38 

255100 

1207 

744900 

48 

13 

248883 

1167 

993059 

38 

255824 

1205 

744176 

47 

14 

249583 

1165 

993036 

38 

256547 

1203 

743453 

46 

15 

250282 

1163 

993013 

38 

257269 

1201 

742731 

45 

16 

250980 

1161 

992990 

38 

257990 

1200 

742010 

44 

17 

251677 

1159 

992967 

38 

258710 

1198 

741290 

43 

18 

252373 

1158 

992944 

38 

259429 

H96 

740571 

42 

19 

253067 

1156 

992921 

38 

260146 

1194 

739854 

41 

20 

253761 

1154 

992898 

38 

260863 

1192 

739137 

40 

21 

9.254453 

1152 

9.992875 

38 

9.261578 

1190 

10.738422 

39 

22 

255144 

1150 

992852 

38 

262292 

1189 

737708 

38 

23 

255834 

1148 

992829 

39 

263005 

1187 

736995 

37 

24 

256523 

1146 

992806 

39 

263717 

1185 

736283 

36 

25 

257211 

1144 

992783 

39 

264428 

1183 

735572 

35 

26 

257898 

1142 

992759 

39 

265138 

1181 

734862 

34 

27 

258583 

1141 

992736 

39 

265847 

1179 

734153 

33 

28 

259268 

1139 

992713 

39 

266555 

1178 

733445 

32 

r>r> 

O(^OQP;I 

1  1^7 

992690 

39 

267261 

1176 

732739 

31 

30 

260633 

1  135 

992666 

39 

267967 

1174 

732033 

30 

31 

9.261314 

1133 

9.99264*3 

39 

9.268671 

1172 

10.731329 

29 

32 

261994 

1131 

992619 

39 

269375 

1170 

73062.5 

28 

33 

262673 

1130 

992596 

39 

270077 

1169 

729923 

27 

34 

263351 

1128 

992572 

39 

270779 

1167 

729221 

26 

35 

264027 

1126 

992549 

39 

271479 

1165 

728521 

25 

36 

264703 

1124 

992525 

39 

272178 

1164 

727822 

24 

37 

265377 

1122 

992501 

39 

272876 

1162 

727124 

23 

38 

266051 

1120 

992478 

40 

273573 

1160 

726427 

22 

39 

266723 

1119 

992454 

40 

274269 

1158 

725731 

21 

40 

267395 

1117 

992430 

40 

274964 

1157 

725036 

20 

41 

9.268065 

1115 

9.992406 

40 

9.275658 

1155 

0.724342 

19 

42 

268784 

1113 

992382 

40 

276351 

1153 

723649 

18 

43 

269402 

1111 

992359 

40 

277043 

1151 

722957 

17 

44 

270069 

1110 

992335 

40 

277734 

1150 

722266 

16 

45 

270735 

1108 

992311 

40 

278424 

1148 

721576 

15 

46 

271400 

1106 

992287 

40 

279113 

1147 

720887 

14 

47 

272064 

1105 

992263 

40 

279801 

1145 

720199 

13 

48 

272726 

1103 

992239 

40 

280488 

1143 

719512 

12 

49 

273388 

1101 

992214 

40 

281174 

1141 

718826 

11 

50 

274049 

1099 

992190 

40 

281858 

1140 

718142 

10 

51 

9.274708 

1098 

9.992166 

40 

9.282542 

1138 

0.717458 

9 

52 

275367 

1096 

992142 

40 

283225 

1136 

716775 

8 

53 

276024 

1094 

992117 

41 

283907 

1135 

716093 

7 

54 

276681 

1092 

992093 

41 

284588 

1133 

715412 

6 

55 

277337 

1091 

9S2069 

41 

285268 

1131 

714732 

5 

56 

277991 

1089 

992044 

41 

285947 

1130 

714053 

4 

57 

278644 

1087 

992020 

41 

286624 

1128 

713376 

3 

58 

279297 

1086 

991996 

41 

287301 

1126 

712699 

2 

59 

279948 

1084 

991971 

41 

287977 

1125 

712023 

1 

60 

280599 

1082 

991947 

41 

288652 

1123 

711348 

0 

Cosine   ( 

Siuo 

Colung.  | 

Tang. 

M. 

79«Degrees, 


SINES  AND  TANGENTS.     ( 1 1   Degrees.) 


M. 

Sine   |   P.     Cosim;   |  I).    Tang.   |   D.   |   Cotang.   | 

0 

9.280599 

1082 

9.991947 

41 

9.288652 

1123 

10.711348 

60 

1 

281248 

1081 

991922 

41 

289326 

1122 

710674 

59 

2 

281897 

1079 

991897 

41 

289999 

1120 

710001 

58 

3 

282544 

1077 

991873 

41 

290671 

1118 

709329 

57 

4 

283190 

1076 

991848 

41 

291342 

1117 

708658 

56 

5 

283836 

1074 

991823 

41 

292013 

1115 

707987 

55 

6 

284480 

1072 

991799 

41 

292682 

1114 

707318 

54 

7 

285124 

1071 

991774 

42 

293350 

1112 

.   7066£0 

53 

8 

285766 

1069 

991749 

42 

294017 

1111 

705983 

52 

9 

286408 

1067 

991724 

42 

294684 

1109 

705316 

51 

10 

287048 

1066 

991699 

42 

295349 

1107 

704651 

50 

11 

9.287687 

1064 

9.991674 

42 

9.296013 

1106 

10.703987 

49 

12 

288326 

1063 

991649 

42 

296677 

1104 

703323 

48 

13 

288964 

1061 

991624 

42 

297339 

1103 

702661 

47 

14 

289600 

1059 

991599 

42 

298001 

1101 

701999 

46 

15 

290236 

1058 

991574 

42 

2'jS662 

1100 

701338 

45 

16 

2908  70 

1056 

931549  12 

2U9322 

1098 

700G73 

44 

17 

291504 

1054 

991524 

42 

299980 

1096 

700020 

43 

13 

292137 

1053 

991498 

42 

300638 

1095 

699362 

42 

19 

292768 

1051 

991473 

42 

301295 

1093 

698705 

41 

2') 

293399 

1050 

991448 

42 

301951 

1092 

698049 

40 

11 

9.294029 

1043 

y.  99  1422 

42 

9.302607 

1090 

10.697393 

39 

22 

2J4658 

1046 

991307 

42 

30326  1 

1089 

696739 

38 

23 

2952SG 

1045 

9913/2 

43 

303914 

1037 

696086 

37 

24 

295913 

1043 

991346 

43 

304567 

1086 

695433 

36 

25 

296539 

1042 

991321 

43 

305218 

1084 

694782 

35 

26 

297164 

1040 

901295 

43 

305369 

1083 

694131 

34 

27 

2977S8 

1039 

991270 

43 

306519 

1081 

693481 

33 

28 

298412 

1037 

991244 

43 

307168 

1080 

692832 

32 

21) 

299034 

1036 

991218 

43 

307815 

1078 

692185 

31 

30 

299655 

1034 

991193 

43 

308463 

1077 

691537 

30 

31 

9  .  300276 

1032 

9.991167 

43 

9.309109 

1075 

10.690891 

29 

32 

300895 

1031 

991141 

43 

309754 

1074 

690246 

28 

33 

30L514 

1029 

991115  43 

310398  1073 

6d9o02 

27 

34 

302132 

1028 

991090  43 

31lOt2!  1071 

6SS9r/8 

26 

35 

302748 

1026 

991064!  43 

311685 

1070 

6883  L  5 

25 

36 

303364 

1025 

991038 

43 

318327 

!0u3 

687073 

24 

37 

303979 

1023 

991012 

43 

312967 

1067 

687033 

23 

38 

304593 

1022 

990986 

43 

313608 

1065 

686392 

22 

39 

305207 

1020 

990960  43 

314247 

1064 

685753 

21 

40 

305819 

1019 

990934 

44 

314885 

1062 

685115 

20 

41 

9.306430 

1017 

9.990908 

44 

9.315523 

1061 

10.684477 

19 

42 

307041 

1016 

990882  44 

316159 

1060 

683841 

18 

43 

307650 

1)14 

990855 

44 

316795 

1058 

683205 

17 

44 

308259 

1013 

990829 

44 

317430 

1057 

682570 

16 

45 

308867 

1011 

990803 

44 

318064 

1055 

681936 

15 

46 

309474 

i-nq 

990777  44 

318697 

1054 

681303 

14 

47 

310080 

1008 

990750  44 

319329 

1053 

680671 

13 

48 

310635 

1007 

990724  44 

319961 

1051 

680039 

12 

49 

311289 

1005 

990697  44 

320592 

1050 

679408 

11 

50 

311S93 

1004 

990671;  44 

3212221  1048 

678778 

10 

51 

9.312495 

1003 

9.990644  44 

9.321851   1047 

10.678149 

9 

52 

313097 

1001 

990618  44 

322479   1045 

677521 

8 

53 

313698 

1000 

990591  44 

323106   1044 

676894 

7 

54 

314297 

998 

990565  44  1   323733   1043 

676267 

G 

55 

314897 

997 

990538  44    324358   1041 

675642 

5 

5G 

315495 

996 

990511  45    324983   1040 

675017 

4 

57 

31  6092  !   994  |   990485  45  !   325607  1039 

674393 

3 

58 

3166891   993    990458  45    326231   1037  !   673769 

2 

59 

317284   991    99043145   326853  1036  i   673147 

60    317879   990    990404  45   327475   1035    672525 

Q 

Cosine  1       '   Sine       |  Cotan-i.            Tang. 

3* 


78  Degrees. 


30 


(I 2  Degrees.)     A  TABLE  OF  LOGARITHMIC 


M,  |    Sine      D.   |   Cosine   |  D. 

Tang. 

D.      Cotang. 

0 

9.317879 

990 

9.990404 

45 

9.327474 

1035 

10.672526 

60 

1 

318473 

988 

990378 

45 

328095 

1033 

671905 

59 

2 

319066 

987 

990351 

45 

328715 

1032 

671285 

58 

3 

319658 

986 

990324 

45 

329334 

1030 

670666 

57 

4 

320249 

984 

990297 

45 

329953 

1029 

670047 

56 

5 

320840 

983 

990270 

45 

330570 

1028 

669430 

55 

6 

321430 

982 

990243 

45 

331187 

1026 

668813 

54 

7 

3122019 

980 

990215 

45 

331803 

1025 

668197 

53 

8 

322607 

979 

990188 

45 

332418 

1024 

667582 

52 

9 

323194 

977 

990161 

45 

333033 

1023 

666967 

51 

10 

323780 

976 

990134 

45 

333646 

1021 

666354 

50 

11 

9.324366 

975 

9.990107 

46 

9.334259 

1020 

10.665741 

49 

12 

324950 

973 

990079 

46 

334871 

1019 

665129 

48 

13 

325534 

972 

990052 

46 

335482 

1017 

664518 

47 

14 

326117 

970 

990025 

46 

336093 

10  J  6 

663907 

46 

15 

326700 

965) 

98U997 

46 

336702 

1015 

663298 

45 

16 

327281 

968 

989970 

46 

337311 

1013 

662689 

44 

17 

327862 

966 

989942 

46 

337919 

1012 

662081 

43 

18 

328442 

965 

'  989915 

46 

338527 

1011 

661473 

42 

19 

329021 

964 

989887 

46 

339133 

1010 

660867 

41 

20 

329599 

962 

989860 

46 

339739 

1008 

G60261 

40 

21 

9.330176 

.961 

9.989832 

46 

9.340344 

1007 

10.659656 

39 

22 

330753 

960 

989804 

46 

340948 

1006 

659052 

38 

23 

331329 

958 

989777 

46 

341552 

1004 

658448 

37 

24 

331903' 

957 

989749 

47 

342155 

1003 

657845 

36 

25 

332478J  956 

989721 

47 

342757 

1002 

657243 

35 

26 

333051 

954 

989693 

47 

343358 

1000 

656642 

34 

27 

333624 

953 

989665 

47 

343958 

999 

658042 

33 

28 

334195 

952 

989637 

47 

344558 

998 

655442 

32 

29 

334766 

950 

989609 

47 

345157 

997 

654843 

31 

30 

335337 

949 

989582 

47 

345755 

996 

654245 

30 

31 

9.335906!  948 

9.989553  47 

9.346353 

994 

JO.  653647 

29 

32 

33647  5  i  946 

989525 

47 

346949 

993 

653051 

28 

33 

337043   945 

989497 

47 

347545 

992 

652455 

27 

34 

3376]  0!  944 

989469 

47 

34814.1 

991 

651859 

26 

35 

338176 

943 

989441 

47 

348735 

990 

651265 

25 

36 

338742 

941 

989413  47 

349329 

988 

6.50671 

24 

37 

339306   940 

989384 

47 

349922 

987 

650078 

23 

38 

339871   939 

989356 

47 

350514 

986 

649486 

22 

39 

340434   937 

989328 

47 

351106 

985 

64*894 

21 

40 

340996   936 

989300 

47 

351697 

983 

648303 

20 

41 

9.  34  j  558 

935 

9.989271 

47 

9.352287 

982 

10.647713 

19 

42 

342119 

934 

989243 

47 

352876 

981 

647124 

18 

43 

3426791  932 

989214 

47 

353465 

980 

646535 

17 

44 

3432391  931 

989186 

47 

354053 

979 

645947 

16 

45 

3437971  930 

989157 

47 

354640 

977 

645360 

15 

46 

344355J  929 

989128 

48 

355227 

976 

644773 

14 

47 

344912!  927 

989100 

48 

355813 

975 

644187 

13 

48 

345469!  926 

989071 

48 

356398 

974 

643602 

12 

49 

3460241  925 

989042 

48 

356982 

973 

643018 

11 

50 

346579;  924 

989014 

48 

357566 

971 

642434 

lO 

51 

9.  3471  34  1  922 

9.988985 

48 

9.358149 

970 

io764l851 

9 

52 

3476871  921 

988956 

48 

358731 

969 

641269 

8 

53 

3482401  920 

988927 

48 

359313 

968 

640687 

7 

54 

3487921  919 

988898 

48 

359893 

967 

640107 

6 

55 

349343 

917 

988869  48 

360474 

966 

639526 

5 

56 

349893 

916 

988840  48 

361053 

965 

638947 

4 

57 

350443 

915 

988811  49 

361632 

963 

638368 

3 

58 

350992 

914 

9887821  49 

362210 

962 

637790 

2 

59 

351540 

913 

988753  49 

362787 

961 

637213 

] 

60 

352088 

911 

988724!  49 

363364 

960 

63663C 

0 

Cosine 

|   Sine 

Cutang.          |    Tang    M. 

77  Degrees 


SINES  AND  TANGENTS.     ^13  Degrees.) 


31 


M.|   Sine   |   D. 

Cosine   |  D.  |   Tang.   |   D.  |   Cotang. 

0 

9.352088 

911 

9.988724 

49 

9.363364 

960 

10.636636 

60 

1 

352635 

910 

988695 

49 

363940 

959 

636060 

59 

2 

353181 

909 

988666 

49 

364515- 

958 

635435 

58 

3 

353726 

908 

988636 

49 

365090 

957 

634910 

57 

4 

354271 

907 

988607 

49 

365664 

955 

634336 

56 

5 

354815 

905 

988578 

49 

366237 

954 

633763 

55 

6 

355358 

904 

988548 

49 

366810 

953 

633190 

54 

7 

355901 

903 

988519 

49 

367382 

952 

632618 

53 

8 

356443 

902 

988489 

49 

367953 

951 

632047 

52 

9 

356984 

901 

988460 

49 

368524 

950 

631476 

51 

10 

'357524 

899 

988430 

49 

369094 

949 

630906 

50 

11 

9.358064 

898 

9.988401 

49 

9.369663 

948 

10.630337 

49 

12 

358603 

897 

988371 

49 

370232 

946 

629768 

48 

13 

359141 

896 

988342 

49 

370799 

945 

629201 

47 

14 

359678 

895 

988312 

50 

371367 

944 

628633 

46 

15 

360215 

893 

988282 

50 

371933 

943 

628067 

45 

16 

360752 

892 

988252 

50 

372499 

942 

627501 

44 

17 

361287 

891 

988223 

50 

373064 

941 

626936 

43 

18 

361822 

890 

988193 

50 

373629 

940 

626371 

42 

19 

362356 

889 

988163 

50 

374193 

939 

625807 

41 

20 

362889 

888 

988133 

50 

374756 

938 

625244 

40 

21 

9.363422 

887 

9.988103 

50" 

9.375319 

937 

10.624681 

39 

22 

363954 

885 

988073 

50 

375881 

935 

624119 

38 

23 

364485 

884 

983043 

50 

376442 

934 

623558 

37 

24 

365016 

883 

938013 

50 

377003 

933 

622997 

36 

25 

365546 

882 

987983 

50 

377563 

932 

622437 

35 

26 

366975 

881 

987953 

50 

378122 

931 

621878 

34 

27 

366604 

880 

987922 

50 

378681 

930 

621319 

33 

28 

367131 

879 

987892 

50 

379239 

929 

620761 

32 

29 

367659 

877 

987862 

50 

379797 

928 

620203 

31 

30 

368185 

876 

987832 

51 

380354 

927 

619646 

30 

31 

9.368711 

875 

9.987801 

51 

9.380910 

926 

W.6  1  9090 

29 

32 

369236 

874 

987771 

51 

381466 

925 

618534 

28 

33 

369761 

873 

987740 

51 

332020 

924 

617980 

27 

34 

370285 

872 

987710 

51 

332575 

923 

617425 

26 

35 

370803 

871 

987679 

51 

383129 

922 

616871 

25 

36 

371330 

870 

987649 

51 

383682 

921 

616318 

24 

37 

371852 

869 

987618 

51 

334234 

920 

615766 

23 

38 

372373 

867 

987538 

51 

384786 

919 

615214 

22 

39 

372894 

866 

987557 

51 

385337 

918 

614663 

21 

40 

373414 

865 

987526 

51 

335888 

917 

614112 

20 

41 

9.373933 

864 

9.987496 

51 

9.386438 

915 

10.613562 

19 

42 

374452 

863 

987465 

51 

38698  7 

914 

613013 

18 

43 

374970 

862 

987434 

51 

337536 

913 

612464 

17 

44 

375487 

861 

937403 

52 

388084 

912 

611916 

16 

45 

376003 

860 

937372 

52 

338631 

911 

611369 

15 

46 

376519 

859 

987341 

52 

389178 

910 

610822 

14 

47 

377035 

858 

997310 

52 

389724 

909 

610276 

13 

48 

377549 

857 

937279 

52 

390270 

908 

609730 

12 

49 

378063 

856 

987248 

52 

390815 

907 

609185 

11 

50 

378577 

854 

987217 

52 

391360 

906 

603640 

10 

51 

9.379089 

853 

9.987186 

52 

9.391903 

905 

10.608097 

9 

52 

379601 

852 

987155 

52 

392447 

904 

607553 

8 

53' 

380113   851 

987124 

52 

392989 

903 

607011 

7 

54 

380624J  850 

987092 

52 

393531 

902 

606469 

6 

55 

381134   849 

987061 

52 

394073 

901 

605927 

5 

56 

381643 

848 

987030 

52 

394614 

900 

605386 

4 

57 

382152 

847 

986993 

52 

395154 

899 

604846 

3 

58 

382661 

846 

986967 

52 

395694 

893 

604306 

2 

59 

383168 

845 

9S6936 

52 

396233 

897 

603767 

1 

60 

383675 

844 

986904 

52 

396771 

896 

603229 

0 

|   Cosine             Sine    I 

Cotang.  I 

Tang. 

M. 

76  Degrees. 


(14  Degrees.;     A  TABLE  OF  LOGARITHMIC 


M. 

Sine 

P.   |  Cosine    D.  |   Tang.   |   D.     Cotang. 

0 

9.383675 

844 

9.986904 

52 

9.396771 

896 

10.603229 

60 

1 

384182 

843 

986873 

53 

397309 

896 

602691 

59 

2 

384687 

842 

986841 

53 

397846 

895 

602154 

58 

3 

385192 

841 

986809 

53 

398383 

894 

601617 

57 

4 

385697 

840 

986778 

53 

398919 

893 

601081 

56 

5 

386201 

839 

986746 

53 

399455 

892 

600545 

55 

6 

386704 

838 

986714 

53 

399990 

891 

600010 

54 

7 

387207 

837 

936683 

53 

400524 

890 

599476 

53 

8 

387709 

836 

986651 

53 

401058 

889 

598942 

52 

9 

388210 

835 

986619 

53 

401591 

888 

598409 

51 

10 

388711 

834 

986587 

53 

402124 

887 

597876 

50 

11 

9.389211 

833 

9.986555 

53 

9.402656 

886 

10.597344 

49 

12 

389711 

832 

986523 

53 

1  403187 

885 

596813 

48 

13 

390210 

831 

986491 

53 

403718 

884 

596282 

47 

14 

390708   830 

986459 

53 

404249 

883 

595751 

46 

15 

.  391206   828 

986427 

53 

404778 

882 

595222 

45 

16 

391703 

827 

986395 

53 

405308 

881 

594692 

44 

17 

392199 

826 

986363 

54 

405836 

880 

594164 

43 

18 

392695 

825 

986331 

54 

406364 

879 

593636 

42 

19 

393191   824 

986299 

54 

406892 

878 

593108 

41 

20 

393685 

823 

986266 

54 

407419 

877 

592581 

40 

21 

9.394179 

822 

9.986234 

54 

9.407945 

876 

10.592055 

39 

22 

394673 

821 

986202 

54 

408471 

875 

591529 

38 

23 

3951661  820 

986169 

54 

408997 

874 

591003 

37 

24 

395658 

819 

986137 

54 

409521 

874 

590479 

36 

25 

396150 

818 

986104 

54 

410045 

873 

589955 

35 

26 

396641 

817 

986072 

54 

410569 

872 

589431 

34 

27 

397132 

817 

986039 

54 

411092 

871 

588908 

33 

28 

397621 

816 

986007 

54 

411615 

870 

588385 

32 

29 

398111 

815 

985974 

54 

412137 

869 

587863 

31 

30 

398600 

814 

985942 

54 

412658 

868 

587342 

30 

31 

9.399088 

813 

9.985909 

55 

9.413179 

867 

10.586821 

29 

32 

399575 

812 

985876 

55 

413699 

866 

586301 

28 

33 

400062 

811 

985843 

55 

414219 

865 

585781 

27 

34 

400549 

810 

985811 

55 

414738 

864 

585262 

26 

35 

401035 

809 

985778 

55 

415257 

864 

584743 

25 

36 

401520 

808 

985745 

55 

415775 

863 

584225 

24 

37 

402005 

807 

985712 

55 

416293 

862 

583707 

23 

38 

402489 

806 

98567G 

55 

416810 

861 

583190 

22 

33 

402972 

805 

985646 

55 

417326 

860 

582674 

21 

40 

403455 

804 

985613 

55 

417842 

859 

582158 

20 

41 

9.403938 

803 

9.985580 

55 

9.418358 

858 

10.581642 

19 

42 

404420 

802 

985547 

55 

418873 

857 

581127 

18 

43 

404901 

801 

985514 

55 

419387 

856 

580613 

17 

44 

405382 

800 

985480 

55 

419901 

855 

580099 

16 

45 

405862 

799 

985447 

55 

420415 

855 

579585 

15 

46 

406341 

798 

985414 

56 

420927 

854 

579073 

14 

47 

406820 

797 

985380 

56 

421440 

853 

578560 

13 

48 

407299 

796 

985347 

56 

421952 

852 

578048 

12 

49 

407777 

795 

985314 

56 

422463 

851 

577537 

11 

50 

408254 

794 

985280 

56 

422974 

850 

577026 

10 

51 

9.4087311  794 

9.985247 

56 

9.423484 

849 

10.576516 

9 

52 

409207 

793 

985213 

56 

423993 

848 

576007 

8 

53 

409682 

792 

985180 

56 

424503 

848 

575497 

7 

54 

4101571  791 

985146 

56 

425011 

847 

574989 

6 

55 

410632   790 

985113 

56 

425519 

846 

574481 

5 

56 

411106   789 

985079 

56 

426027 

845 

573973 

4 

57 

411579   788 

985045 

56 

426534 

844 

573466 

3 

58 

412052i   787 

985011 

56 

427041   843 

572959 

2 

59 

412524 

786 

984978 

56 

•  427547 

843 

572453 

1 

60 

412996 

785 

984944 

56 

428052 

842 

571948 

0 

Cof-ine 

Sine 

j  Co.mig.  | 

Tang 

M. 

75  Degrees. 


SINES  AND  TANGENTS.       (15  Degrees.) 


33 


RL|    Sine   |   D. 

Cosine    D.    Tang.  |   D.  |   Cotana.  j 

0 

9.412996 

785 

9  .  984944 

5V 

9.428052 

842 

10.571948 

bO 

1 

413467 

784 

984910 

57 

428557 

841 

571443 

59 

a. 

413938 

783 

984876 

57 

429062 

840 

570938 

58 

3 

414408 

783 

984842 

57 

429566 

839 

570434  57 

4 

414878 

782 

984808 

57 

430070 

838 

569930 

56 

5 

415347 

781 

984774 

57 

430573 

838 

569427 

55 

6 

415815 

780 

984740 

57 

431075 

837 

568925 

54 

7 

416283 

779 

9S4706 

57 

431577 

836 

568423 

53 

8 

416751 

778 

984672 

57 

432079 

835 

567921 

52 

9 

417217 

777 

984637 

57 

432580 

834 

567420 

51 

10 

417684 

770 

984603 

57 

4330SO 

833 

566920 

50 

11 

9.418150 

775 

9.984569ff? 

9.433580   832 

10:566420 

49 

12 

418615 

774 

984535157 

434080 

832 

565920 

48 

13 

419079 

773 

984500 

57 

434579 

831 

565421 

47 

14 

419544 

773 

984466 

57 

435078 

830 

564922 

46 

15 

420007 

772 

984432 

58 

435576 

829 

564424 

45 

16 

420470 

771 

984397 

58 

436073 

828 

563927 

44 

17 

420933 

770 

984363 

58 

436570 

828 

563430 

43 

18 

421395 

769 

984328 

58 

437067 

827 

562933 

42 

19 

421857 

768 

984294 

58 

437563 

826 

562437 

41 

20 

422318 

767 

984259 

58 

438059 

825 

561941 

40 

21 

9  422778 

767 

9.984224 

58 

9.438554 

824 

10.561446 

39 

22 

423238 

766 

984190 

58 

439048 

823 

560952 

38 

23 

423697 

765 

984155 

58 

439543 

823 

560457 

37 

24 

424156 

764 

984120 

58 

440036 

822 

559964 

36 

25 

424615 

763 

984085 

58 

440529 

821 

559471 

35 

26 

425073 

762 

984050 

58 

441022 

820 

558978 

34 

27 

425530 

761 

984015 

58 

441514 

819 

558486 

33 

28 

425987 

760 

983981 

58 

442006 

819 

557994 

32 

29 

426443 

760 

983946 

58 

442497 

818 

557503 

31 

30 

426899 

759 

983911 

58 

442988 

817 

557012 

30 

31 

9.427354 

758 

9.983875 

58 

9.443479 

816 

10.556521 

29 

32 

427809 

757 

983840 

59 

443968 

816 

556032 

28 

33 

428263 

756 

983805 

59 

444458 

815 

555542 

27 

34 

428717 

755 

98377K) 

59 

444947 

814 

555053 

26 

35 

429170 

754 

983735 

59 

445435 

813 

554565 

25 

36 

429623 

753 

983700J  59 

445923 

812 

554077 

24 

37 

430075 

752 

983664 

59 

44641  1 

812 

553589 

23 

38 

430527 

752 

983629 

59 

446898 

811 

553102 

22 

39 

430978 

751 

983594 

59 

447384 

810 

552616 

21 

40 

431429 

750 

983558 

59 

447870 

809 

552130 

20 

41 

9.431879 

749 

9.983523 

59 

9.448356 

809 

10.551644 

19 

42 

432329 

749 

983487 

59 

448841 

808 

551159 

18 

43 

432778 

748 

983452 

59 

449326 

807 

550674 

17 

44 

433226 

747 

983416 

59 

449810 

806 

550190 

16 

45 

433675 

746 

983381 

59 

450294 

806 

549706 

15 

46 

434122 

745 

983345 

59 

450777 

805 

549223 

14 

47 

434569 

744 

983309 

59 

451260 

804 

548740 

13 

48 

435016 

744 

983273 

60 

451743 

803 

548257 

12 

49 

435462 

743 

983238 

60 

452225 

802 

547775 

11 

50 

435908 

742 

983202 

60 

452706 

802 

547294 

10 

51 

9.436353 

741 

9.983166 

60 

9.453187 

801 

10.546813 

9 

52 

436798 

740 

983130 

60 

453668 

800 

546332 

8 

53 

437242 

740 

983094 

60 

454148 

799 

545852 

7 

54 

437686 

739 

983058 

60 

454628 

799 

545372 

6 

55 

438129 

738 

983022 

60 

455107 

798 

544893 

5 

56 

438572 

737 

982986 

60 

455586 

797 

544414 

4 

57 

439014 

736 

982950 

60 

456064 

796 

543936 

3 

58 

439456 

736 

982914 

60 

456542 

796 

543458 

2 

59 

439897 

735 

982878!  60 

457019 

795 

542981 

1 

60 

440338 

734 

982842!  60 

457496 

794 

542504 

0 

Cosine 

Sine   | 

Cotang.  |       |    Tang.   |  M. 

74  Degrees. 


34 


(16  Degrees.)     A  TABLE  OF  LOGARITHMIC 


M.     Sine     D.     Cosine  |  D.    Tang.   |   D. 

Cotang. 

0 

9.440338 

734 

9.982842 

60  I  9.457496 

794 

10.542504 

60 

1 

440778 

733 

982805 

60    457973 

793 

542027 

59 

2 

441218 

732 

982769 

61    45«449 

793 

541551 

58 

3 

441658 

731 

982733 

61    458925 

792 

541075 

57 

4 

442096 

731 

982696 

61    459400 

791 

540600 

56 

5 

442535 

730 

982660 

61    459875 

790 

540125 

55 

6 

442973 

729 

982624 

61    460349 

790 

539651 

54 

7 

443410 

728 

982587 

61    460323 

789 

539177 

53 

8 

443847 

727 

982551 

61    461297 

788 

538703 

52 

9 

444284 

727 

982514 

61    461770 

788 

538230 

fl 

10 

444720 

726 

982477 

61  |   462242 

787 

537758 

50 

11 

9.445155 

725 

9.982441 

61  if.  462714 

786 

10.537286 

49 

12 

445590 

724 

982404 

61    463186 

785 

536814 

48 

13 

446025 

723 

982367 

61    463658 

785 

536342 

47 

14 

446459 

723 

982331 

61    464129 

784 

535871 

46 

15 

446893 

722 

982294 

61    464599 

783 

535401 

45 

16 

447326 

721 

982257 

61    465069 

783 

534931 

44 

17 

447759 

720 

982220 

62   465539 

782 

534461 

43 

18 

448191 

720 

982183 

62 

466008 

781 

533992 

42 

19 

448623 

719 

982146 

62 

466476 

780 

533524 

41 

20 

449054 

718 

982109 

62 

466945 

780 

533055 

40 

21 

9.449485 

717 

9.982072 

62 

9.467413 

779 

10.532587 

39 

22 

449915 

716 

982035 

62 

467880 

778 

532120 

38 

23 

450345 

716 

981998 

62 

468347 

778 

531-653 

37 

24 

450775 

715 

981961 

62 

468814 

777 

531186 

36 

25 

451204 

714 

981924 

62 

469280 

776 

530720 

35 

26 

451632 

713 

981886 

62 

469746 

775 

530254 

34 

27 

452060 

713 

981849 

62 

470211 

775 

529789 

33 

28 

452488 

712 

981812 

62 

470676 

774 

529324 

32 

29 

452915 

711 

981774 

62 

471141 

773 

528859 

31 

30 

453342 

710 

981737 

oa 

47  1605 

773 

528395 

30 

31 

9.453768 

710 

9.981699 

63 

9.472068 

772 

10.527932 

29 

32 

454194 

709 

981662 

63 

472532 

771 

527468 

28 

33 

454619 

708 

981625 

63 

472995 

771 

527005 

27 

34 

455044 

707 

981587 

63 

473457 

770 

526543 

26 

35 

455469 

707 

981549 

63 

473919 

769 

526081 

25 

36 

455893 

706 

981512 

63 

474381 

769 

525619 

24 

37 

456316 

705 

.  981474 

63 

•  474842 

768 

525158 

23 

38 

456739 

704 

981436 

63 

475303 

767 

524697 

22 

39 

457162 

704 

981399 

63 

475763 

767 

524237 

21 

40 

457584 

703 

981361 

63 

476223 

766 

523777 

20 

41 

9:458006 

702 

9.981323 

63 

9.476683 

765 

10.523317 

19 

42 

458427 

701 

981285 

63 

477142 

765 

522858 

18 

43 

458848 

701 

981247 

63 

477601 

764 

522399 

17 

44 

459268 

700 

981209 

63 

478059 

763 

521941 

16 

45 

459688 

699 

981171 

63 

478517 

763 

521483 

15 

46 

460108 

698 

981133 

64 

478975 

762 

521025 

14 

47 

460527 

698 

981095 

64 

479432 

761 

520568 

13 

48 

460946 

697 

981057 

64 

479889 

761 

520111 

12 

49 

461364 

696 

981019 

64 

480345 

760 

519655 

11 

50 

461782 

695 

980981 

64 

480801 

759 

519199 

10 

51 

9.462199 

695 

9.980942 

64 

9.481257 

759 

10.518743 

9 

52 

462616 

694 

980904 

64 

481712 

758 

518288 

8 

53 

463032 

693 

980866 

64 

482167 

757 

517833 

7 

54 

463448 

693 

980627 

64 

482621 

757 

517379 

6 

55 

46386^. 

692 

980789 

64 

483075 

756 

516925 

5 

56 

464279 

691 

980750 

64 

483529 

755 

516471 

4 

57 

464694 

690 

980712 

64 

483982 

755 

516018 

3 

58 

465108 

690 

980673 

64 

484435 

754 

515565 

2 

59 

465522 

689 

980635 

64 

484887 

753 

515113 

1 

60 

465935 

688 

980596''  64 

485339 

753 

5l4fifil 

0 

Cosine 

|   Sine 

Cotang. 

Tang. 

M. 

73  Degrees. 


SINES  AND  TANGENTS.     (11  Degrees.) 


M.  |   Sine   |   D   j   Cosine   |  D.  |   Tang.      D.  |   Cotang. 

o 

9.465935 

688 

9.980596 

64 

9.485339 

755 

10.514661 

bO 

1 

466348 

688 

980558 

64 

485791 

752 

514209 

59 

2 

466761 

687 

980519 

65 

486242 

751 

513758 

58 

3 

467173 

686 

980480 

65 

486693 

751 

513307 

57 

4 

467585 

685 

980442 

65 

487143 

750 

512857 

56 

5 

467996 

685 

980403 

65 

487593 

749 

512407 

55 

6 

468407 

684 

980364 

65 

488043 

749 

511957 

54 

7 

468817 

683 

980325 

65 

488492 

748 

511508 

53 

8 

469227 

683 

980286 

65 

488941 

747 

511059 

52 

9 

469637 

682 

980247 

65 

489390 

747 

510610 

51 

10 

470046 

681 

980208 

65 

489838 

746 

510162  50 

11 

9  .  470455 

680 

9.980169 

65- 

9.490286 

746 

10.509714 

49 

12 

470863 

680 

980130 

65* 

490733 

745 

509267 

48 

13 

471271 

679 

980091 

65 

491180 

744 

508820 

47 

14 

471679 

678 

980052 

65 

491627 

744 

508373 

46 

15 

472086 

678 

980012 

65 

492073 

743 

507927 

45 

16 

472492 

677 

979973 

65 

492519 

743 

507481 

44 

17 

472898 

676 

979934 

66 

492965 

742 

507035 

43 

18 

473304 

676 

979895 

66 

493410 

741 

506590 

42 

19 

473710 

675 

979855 

66 

493854 

740 

506148 

41 

20 

474115 

674 

979816 

66 

494299 

740 

505701 

40 

21 

9.474519 

674 

9.979776 

66 

9.494743 

740 

10.505257 

39 

22 

474923 

673 

979737 

66 

495186 

739 

504814 

38 

23 

475327 

672 

979697 

66 

495630 

738 

504370 

37 

24 

475730 

672 

979658 

66 

496073 

737 

503927 

36 

25 

476133 

671 

979618 

66 

496515 

737 

503485 

35 

26 

476536 

670 

979579 

66 

496957 

736 

503043 

34 

27 

476938 

669 

979539 

66 

497399 

736 

502601 

33 

28 

477340 

669 

979499 

66 

497841 

735 

502159 

32 

29 

177741 

668 

979459 

66 

498282 

734 

501718 

31 

30 

478142 

667 

979420 

66 

498722 

734 

501278 

30 

31 

9.478542 

667 

9.979380 

66 

9.499163 

733 

10.500837 

29 

32 

478942 

666 

979340 

66 

499603 

733 

500397  28 

33 

479342 

665 

979300 

67 

500042 

732 

499958 

27 

34 

479741 

665 

979260 

67 

500481 

731 

499519 

26 

35 

480140 

664 

979220 

67 

500920 

731 

499080 

25 

36 

480539 

663 

979180 

67 

501359 

730 

49864! 

24 

37 

480937 

663 

979140 

67 

501797 

730 

498203 

23 

38 

481334 

662 

979100 

67 

502235 

729 

497765 

22 

39 

481731 

661 

979059 

67 

502672 

728 

497328  2! 

40 

482128 

661 

979019 

67 

503109 

728 

496891  20 

41 

9  482525 

660 

9.978979 

67 

9.503546 

727 

TO.  496454 

19 

42 

482921 

659 

978939 

67 

503982 

727 

496018 

18 

43 

483316 

659 

978898 

67 

504418 

726 

495582 

17 

44 

483712 

658 

978858 

67 

504854 

725 

495146 

16 

45 

484107 

657 

978817 

67 

505289 

725 

49471  1 

15 

46 

484501 

657 

978777 

67 

505724 

724 

494276 

14 

47 

484895 

656 

978736 

67 

506159 

724 

493841 

13 

48 

485289 

655 

978696 

68 

506593 

723 

493407 

12 

49 

485682 

655 

978655 

68 

507027 

722 

492973 

11 

50 

486075 

654 

978615 

68 

507460 

722 

492540 

10 

51 

9.  -486467 

653 

9.978574 

68 

9.507893 

721 

107492107 

9 

52 

486860 

653 

978533 

68 

508326 

721 

491674 

8 

53 

487251 

652 

978493 

68 

508759 

720 

491241 

7 

54 

487643 

651 

978452 

68 

509191 

719 

490809 

6 

55 

488034 

651 

978411 

68 

509622 

719 

490378 

5 

56 

488424 

650 

978370 

68 

510054 

718 

489946 

4 

57 

488814 

650 

978329 

68 

510485 

718 

489515 

3 

.58 

489204 

649 

978288 

68 

510916 

717 

489084 

2 

59 

489593 

648 

97824? 

68 

511346 

716 

488654 

1 

60 

489982 

648 

978206 

68 

511776 

716 

488224   0 

Cosine   1         Sine   |    |  Cotang.  1           'J  ang.   M. 

72  Degrees. 


(18  Degrees.)     A  TABLE  OF  LOGARITHMIC 


M. 

Sine 

D.   1  Cosine   |  I). 

Tang.  |   D. 

Cotanp. 

0 

9.489982 

648 

9.978206 

68 

9.511776 

716 

10.488224 

60 

1 

490371 

648 

978165 

68 

512206 

716 

487794 

59 

2 

490759 

647 

978124 

68 

5126351  715 

487365 

58 

3 

491147 

646 

978083 

69 

513064   714 

486936 

57 

4 

491535   646 

978042 

69 

513493   714 

486507 

56 

5 

491922,  645 

978001 

69 

513921   713 

486079 

55 

6 

492308 

644 

977959 

69 

514349   713 

485651 

54 

7 

492695 

644 

977918 

69 

514777   712 

485223 

53 

8 

493081 

643 

977877 

69 

515204   712 

484796 

52 

9 

493466 

642 

977835 

69 

5156311   711 

484369 

51 

10 

493851 

642 

977794 

69 

516057   710 

483943 

50 

11 

9.494236 

641 

9.977752 

69 

9.516484   710 

10.483516 

49 

12 

494621 

641 

977711 

*9 

516910   709 

483090 

48 

13 

495005 

640 

977669 

69 

517335,   709 

482665 

47 

14 

495388 

639 

977628 

69 

517761   708 

482239 

46 

15 

495772 

639 

977586 

69 

518185   708 

481815 

45 

16 

496  154 

638 

977544 

70 

518610   707 

481390 

44 

17 

496537 

637 

977503 

70 

519034   706 

480966 

43 

18 

496919 

637 

977461 

70 

519458   706 

480542 

42 

19 

497301 

636 

977419 

70 

519882 

705 

480118 

41 

20 

497682 

636 

977377 

70 

520305 

705 

479695 

40 

21 

9.498064 

635 

9.977335 

70 

9.520728   704 

10.479272 

39 

22 

498444 

634 

977293 

70 

521151   703 

478849 

38 

23 

498825 

634 

977251 

70 

5215731   703 

478427 

37 

24 

499204 

633 

977209 

70 

521995'   703 

478005 

36 

25 

499584 

632 

977167 

70 

522417!   702 

477583 

35 

26 

499963 

632 

977125 

70 

522838 

702 

477162 

34 

27 

500342 

631 

977083 

70 

523259 

701 

476741 

33 

28 

500721 

631 

977041 

70 

523680 

701 

476320 

32 

29 

501099 

630 

976999 

70 

5241  00 

700 

475900 

31 

30 

501476 

629 

976957 

70 

524520 

699 

475480 

30 

31 

9.501854 

629 

9.976914 

70 

9  .  524939 

699 

10.475061 

29 

32 

502231 

628 

976872 

71 

525359 

698 

47464.1 

28 

33 

502607 

628 

976830 

71 

525778 

698 

474222 

27 

34 

502984 

627 

976787 

71 

526197 

697 

473803 

26 

35 

503360 

626 

976745 

71 

526615 

G97 

473385 

25 

36 

503735 

626 

976702 

71 

527033 

696 

472967 

24 

37 

504110 

625 

976660 

71 

527451 

696 

472549 

23 

38 

504485 

625 

976617 

71 

527868 

695 

472132 

22 

39 

504860 

624 

976574 

71 

528285 

695 

471715 

21 

40 

505234 

623 

976502 

71 

528702 

694 

471298 

20 

41 

9.505608 

623 

9.976489 

71 

9.529119 

693 

0.470881 

19 

42 

505981 

622 

976446 

71 

52<>535 

693 

470465 

18 

43 

506354 

622 

970404 

71 

529950 

693 

470050 

17 

44 

506727 

621 

978361 

71 

530366 

692 

469634 

16 

45 

507099 

620 

97G318 

71 

530781 

691 

469219 

15 

46 

507471 

620 

976275 

71 

531196 

691 

468804 

14 

47 

507843 

619 

976232 

72 

531611 

690 

468389 

13 

48 

508214 

619 

970189 

72 

532025 

690 

467975 

12 

49 

508585 

618 

976146 

72 

532439 

689 

467561 

11 

50 

508956 

618 

976103 

72 

532853 

689 

467147 

10 

51 

9.509326 

617 

9.976060 

72 

9.533266 

688 

10.466734 

9 

52 

509696 

61  6 

976017 

72 

533679 

688 

466321 

8 

53 

510065 

616 

975974 

72 

534092 

687 

465908 

7 

54 

510434 

615 

975930 

72 

534504 

687 

465496 

6 

55 

510803 

615 

975887 

72 

534916 

686 

465084 

5 

56 

511172 

614 

975844 

72 

535328 

686 

464672 

4 

57 

511540 

613 

975800 

72 

535739 

685 

464261 

3 

58 

511907 

613 

975757 

72 

536150 

685 

463850 

2 

59 

612275 

612 

975714 

72 

536561 

684 

463439 

1 

60 

512642 

612 

975670 

72 

536972 

684 

463028 

0 

Conine   | 

Sine       1  Cotang.  1 

Tang. 

M. 

7'  Devices. 


SINES   AND    TANGENTS.       (19    Degrees.) 


37 


M. 

Sine   |   D. 

Cosine  |  D.    Tang.   |   D.     Cotang. 

0 

9.512642 

612 

9.975670 

73 

9.536972 

684 

10.463028 

60 

1 

513009 

6il 

975627 

73 

537382 

683 

462618 

59 

2 

513375 

611 

9755S3 

73 

537792 

683 

462208 

58 

3 

513741 

610 

975539 

73 

538202 

682 

461798 

57 

4 

514107 

609 

975496 

73 

538611 

682 

461389 

56 

5 

514472 

609 

975452 

73 

539020 

681 

460980 

55 

6 

514837 

608 

9/5408 

73 

539429 

681 

460571 

54 

7 

515202 

608 

9T5365 

73 

539837 

680 

460163 

53 

8 

515566 

607 

975321 

73 

540245 

680 

469755 

52 

9 

515930 

607 

975277 

73 

540653 

679 

459347 

51 

10 

516294 

6^6 

975233 

73 

541061 

679 

458939 

50 

11 

9.516657 

605 

9.975189 

73 

9.541468 

678 

10.458532 

49 

12 

517020 

605 

975145 

73 

541875 

678 

458125 

48 

13 

517382 

604 

975101 

73 

542281 

677 

457719 

47 

14 

517745 

604 

975057 

73 

542688 

677 

457312 

46 

15 

518107 

603 

975013 

73 

543094 

676 

456906 

45 

16 

518468 

603 

974969 

74 

543499 

676 

456501 

44 

17 

518829 

602 

974925 

74 

543905 

675 

456095 

43 

18 

519190 

601 

974880 

74 

544310 

675 

455690 

42 

19 

519551 

601 

974836 

74 

544715 

674 

455285 

41 

20 

519911 

600 

974792 

74 

545119 

674 

454881 

40 

21 

9.520271 

600 

9.974748 

74 

9.545524 

673 

10.454476 

39 

22 

520631 

599 

974703 

74 

545928 

673 

454072 

38 

23 

520990 

599  , 

974659 

74 

546331 

672 

453669 

37 

24 

521349 

598  , 

974614 

74 

546735]   672 

453265 

36 

25 

521707 

5<*S 

974570 

74 

547138 

671 

452862 

35 

26 

522066 

597 

974525 

74 

547540 

671 

452460 

34 

27 

522434 

596 

974481 

74 

547943 

670 

452057 

33 

28 

522781 

596 

974436 

74 

548345 

670 

451655 

32 

29 

523138 

595 

974391 

74 

548747 

669 

451253 

31 

30 

523495 

595 

974347 

75 

549149 

669 

450851 

30 

31 

9.523852 

594 

9.974302 

75 

9.549550 

668 

10.450450 

29 

32 

524208 

594 

974257 

75 

549951 

668 

450049 

28 

33 

634564 

593 

974212 

75 

550352 

667 

449648 

27 

34 

524920 

593 

974167 

75 

550752 

667 

449248 

26 

35 

525275 

592 

974122 

75 

551152 

666 

448848 

25 

36 

525630 

591 

974077 

75 

551552 

666 

448448 

24 

37 

525984 

591 

974032 

75 

551952 

665 

448048 

23 

38 

526339 

590 

973987 

75 

552351 

665 

447649 

22 

39 

526693 

590 

973942 

75 

552750 

665 

447250 

21 

40 

527046 

589 

973897 

75 

553149 

664 

446851 

20 

41 

9.527400 

589 

9.973852 

75 

9.553548 

664 

T07446452 

19 

42 

527753 

588 

973807 

75 

553946 

663 

446054 

18 

43 

528105 

588 

973761 

75 

554344 

663 

445656 

17 

44 

528458 

587 

973716 

76 

554741 

662 

445259 

16 

45 

528810 

587 

973671 

76 

555139 

662 

444861 

15 

46 

529161 

586 

973625 

76 

555536 

661 

444464 

14 

47 

529513 

586 

973580 

76 

555933 

661 

,444067 

13 

48 

529864 

585 

973535 

76 

556329 

660 

443671 

12 

49 

530215 

585 

973489 

76 

556725 

660 

443275 

11 

50 

030565 

584 

973444 

76 

557121 

659 

442879 

10 

51 

9.530915 

584  9.973398 

76 

9.557517 

659 

10.442483 

9 

52 

531265 

583 

973352 

76 

557913 

659 

442087 

8 

53 

531614 

582 

973307 

76 

558308 

658 

441692 

7 

54 

531963 

582 

973261 

76 

558702 

658 

441298 

6 

55 

532312 

581 

973215 

76 

559097 

657 

440903 

5 

56 

532661 

581 

973169 

76 

559491 

657 

440509 

4 

57 

533009 

580 

973124 

76 

559885 

656 

440115 

3 

58 

533357 

580 

973078 

76 

560279 

656 

439721 

2 

59 

533704 

579 

973032 

77 

560673 

655 

439327 

1 

*0 

534052,   578 

972986 

77 

561066 

655 

438934 

0 

Cosine   |      J   Sine 

Cotang.   | 

Tang.    M. 

70  Degrees. 


38 


(20  Degrees.)     A  TABLE  OP  LOGARITHMIC 


M.    Sine   |   D.    Cosine   |  D.  |   Tang.   f   D.     Cotang.   | 

0 

9.534052)  578  9.972986177 

9.561066 

655 

10.438934 

60 

1 

534399 

577 

972940 

77 

561459 

654 

438541 

59 

2 

534745 

577 

972894 

77 

561851 

654 

438149 

58 

3 

535092 

577 

972848 

77 

562244 

653 

437756 

57 

4 

535438 

576 

9728021  77 

562636 

653 

437364 

56 

5 

535783 

576 

972755 

77 

563028 

653 

436972 

55 

6 

536129 

575 

972709 

77 

563419 

652 

436581 

54 

7 

536474 

574 

972663 

77 

563811 

652 

436189 

53 

8 

536818 

574 

972617 

77 

564202 

651 

435798 

52 

9 

537163 

573 

972570 

77 

564592 

651 

435408 

51 

10 

537507 

573 

972524 

77 

564983 

650 

435017 

50 

11 

9.537851 

572 

9.972478 

77 

9.5653713 

650 

10.434627 

49 

12 

538194 

572 

972431 

78 

565763 

649 

434237 

48 

13 

538538 

571 

972385 

78 

566153 

649 

433847 

47 

14 

538880 

"571 

972338 

78 

566542 

649 

433458 

46 

15 

539223 

570 

972291 

78 

566932 

648 

433068 

45 

16 

539565 

570 

972245 

78 

567320 

648 

432680 

44 

17 

539907 

569 

972198 

78 

567709 

647 

432291 

43 

18 

540249 

569 

972151 

78 

568098 

647 

431902 

42 

19 

540590 

568 

972105 

79 

568486 

646 

431514 

41 

20 

540931 

568 

972058 

78 

568873 

646 

431127 

40 

21 

9.541272 

567 

9.972011 

78 

9.569261 

645 

10.430739 

39 

22 

541613 

567 

971964 

78 

569648 

645 

430352 

38 

23 

541953 

566 

971917 

78 

570035 

645 

429965 

37 

24 

542293 

566 

971870 

78 

570422 

644 

429578 

36 

25 

54263'2 

565 

971823 

78 

570809 

644 

429191 

35 

26 

542971 

565 

971776 

78 

571195 

643 

428805 

34 

27 

543310 

564    971729 

79 

571581 

643 

428419 

33 

28 

543649 

564    971682 

79 

571967 

642 

428033 

32 

29 

543987 

563    971635 

79 

572352 

642 

427648 

31 

30 

544325 

563    971588 

79 

572738 

642 

427262 

30 

31 

9.544663 

562  !  9.971540 

79 

9.573123 

641 

107426877 

29 

32 

545000 

562 

971493 

79 

573507 

641 

426493 

28 

33 

545338 

561 

971446 

79 

573892 

640 

426  1  08 

27 

34 

545674 

561 

971398 

79 

574276 

640 

425724 

26 

35 

546011 

560 

971351 

79 

574660 

639 

425340 

25 

36 

546347 

560 

971303 

79 

575044 

639 

424958 

24 

37 

546683 

559 

971256 

79 

575427 

639 

424573 

23 

38 

547019 

559 

971208 

79 

575810 

638 

424190 

22 

39 

547354 

558 

971161 

79 

576193 

638 

423807 

21 

40 

547689 

558 

971113 

79 

576576 

637 

423424 

20 

41 

9.548024 

557 

9.971066 

80 

9.576958 

637 

10.423041 

19 

42 

548359 

557 

971018 

80 

577341 

636 

422659 

18 

43 

548693 

556 

970970 

80 

577723 

636 

422277 

.7 

44 

549027 

556 

970922 

80 

578104 

636 

421896 

16 

45 

549360 

555 

970874 

80 

578486 

635 

421514 

15 

46 

549693 

555  |   970827 

80 

578867 

635 

421133 

14 

47 

550026 

554    970779 

80 

579248 

634 

420752 

13 

48 

550359 

554  1   970731 

80 

579629 

634 

420371 

12 

49 

550692 

553  j   970683 

80 

580009 

634 

419991 

11 

50 

551024 

553  !   970635 

80 

580389 

633 

419611 

10 

51 

9.551356 

552 

9.970586 

80 

9.580769 

633 

107419231 

9 

52 

551687 

552 

970538 

80 

581149 

632 

418851 

8 

53 

552018 

552 

970490 

80 

581528 

632 

418472 

7 

54 

552349 

551 

970442 

80 

581907 

632 

418093 

6 

55 

552680 

551 

970394 

80 

582286 

631 

417714 

5 

56 

553010 

550 

970345 

81 

582665 

631 

417335 

4 

57 

553341 

550 

970297 

81 

583043 

630 

416957 

3 

58 

553670 

549 

970249 

81 

583422 

630 

416578 

2 

59 

554000 

549 

970200 

81 

583800 

629 

416200 

1 

60 

554329 

54S 

970152 

81 

584177 

629 

415823 

0 

mt 

Cnsiin-   | 

«me    1    |   Ootaup.  | 

Tang.    M. 

Degrees. 


SINES  AND  TANGENTS.     (21  Degrees.; 


39 


M.    Sine   |   D.     Cosine  |  D.    Tang.      D.   |    Cotang.  | 

0 

9.554329 

548  1  9.970152 

81 

9.584177 

629 

0.415823 

01 

1 

554658 

548 

970103 

81 

584555 

629 

415445 

9 

2 

554987 

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970055 

81 

584932 

628 

415068 

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3 

555315 

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970006 

81 

585309 

628 

414691 

7 

4 

555643 

546 

969957 

81 

585686 

627 

4143-14 

6 

5 

555971 

546 

969909 

81 

586062 

627 

413938 

51 

6 

556299 

545 

969860 

81 

586439 

627 

413561 

41 

7 

556626 

545 

969811 

81 

586815 

626 

413185 

3 

8 

556953 

544 

969762 

81 

587190 

626 

412810 

2| 

9 

557280 

544 

969714 

81 

587566 

625 

412434 

1  I 

10 

557606 

543 

969665 

81 

587941 

625 

412059 

° 

11 

9  .  5579S2 

543 

9.969616 

82 

9.588316 

625 

I0o411684 

9 

12 

558258 

543 

969567 

82 

588691 

624 

411309 

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558583 

542 

969518 

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589066 

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410934 

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14 

558909 

542 

969469 

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589440 

623 

410560 

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589814 

623 

410186 

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590188 

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969321 

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590562 

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409438 

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590935 

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409065 

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969223 

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591308 

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408692 

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9.561178 

538 

9.969124 

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9.592054 

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10.407946 

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561501 

538 

969075 

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592426 

620 

407574 

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561824 

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969025 

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592798 

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407202 

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562146 

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968976 

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593170 

619 

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9.564396 

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10.404232 

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968578 

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598354 

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9.570751 

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9.967624 

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9.60312 

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10.396873 

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396507 

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96752S 

85 

60385 

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571  69£ 

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967471 

85 

60422 

608 

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0 

Conine   I          Sine 

|  C'oiang.             Tang.    M.  1 

C8 


(22  Degrees.;     A  TABLE  OF  LOGARITHMIC 


M.  |   Sine      D.    Cosine   |  D.  '   Tang.     D.      Cotang.  | 

0 

9.573575 

521 

9.967166 

85 

9.606410 

606 

10.393590 

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966859 

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391412 

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608950 

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9,610397 

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10.389603 

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10.386000 

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10.378858 

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17 

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,  373555 

4 

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89 

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3 

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497 

964133 

89 

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586 

372851 

2 

59 

591580 

496 

964080 

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627501 

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1 

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5918781  496 

964026 

89 

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585 

372148 

0 

Cosine  j          Sine 

Cotaiiij. 

Tang.   |  M. 

67  Degrees. 


SINES  AND  TANGENTS.      (23  Degrees.) 


41 


M. 

Sine   |   D.     Cosine   |  D.  |   Tang.  |   D.  (   Cotang. 

0 

9.591878 

496 

9.964026 

89 

9.627852 

585 

10.372148 

60 

1 

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495 

963972 

89 

628203 

585 

371797 

59 

2 

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89 

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58 

3 

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628905 

584 

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57 

4 

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90 

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56 

5 

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90 

629606 

583 

370394 

55 

6 

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629956 

583 

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54 

7 

593955 

493 

963650 

90 

630306 

583 

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53 

8 

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583 

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52 

9 

594547 

492 

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631005 

582 

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10 

594842 

492 

963488 

90 

631355 

582 

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50 

11 

9.595137 

491 

9  .  963434 

90 

9.631704 

582 

10.368296 

49 

12 

595432 

491 

963379 

90 

632053 

581 

367947 

48 

13 

595727 

491 

963325 

90 

632401 

581 

367599 

47 

14 

596021 

490 

963271 

90 

632750 

581 

367250 

46 

tfl 

596315   490 

9R3217  90 

633098 

580 

366902 

45 

16 

596609 

489 

903163  90 

633447 

580 

3G6553 

44 

17 

596903 

489 

963108  91 

633795 

580 

366205 

43 

18 

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489 

963054 

91 

634143 

579 

365857 

42 

19 

597490 

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91 

634490 

579 

365510 

41 

20 

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634838 

579 

365162 

40 

21 

9.598075 

487 

9.962890 

91 

9.635185 

578 

10.364815 

39 

22 

598368 

487 

91)2830 

91 

635532 

578 

364468 

38 

23 

5986601  487 

962781 

91 

635879 

578 

364121 

37 

24 

598952   486 

982727 

91 

636226 

577 

363774 

36 

25 

599244   486 

962672 

91 

636572 

577 

363428 

35 

26 

5995361  485 

902617  91 

636919 

577 

363081 

34 

27 

599827 

485 

962562 

91 

637265 

577 

362735 

33 

28 

600118 

485 

962508 

91 

637611 

576 

362389 

32 

29 

600409   484 

962453 

91 

637956 

576 

362044 

31 

30 

600700  i  484 

962398 

92 

638302 

576 

361698 

30 

31 

9.600990   484 

9.962343 

92 

9.638647 

575 

10.361353 

29 

32 

601280   483 

962288  92    63«992 

575 

361008 

28 

33 

601570 

483 

962233  92 

6393371  575 

360663 

27 

34 

601860 

482 

962178!  92 

639682   574 

360318 

26 

35 

602150 

482 

962123!  92 

640027 

574 

359973 

25 

36 

6024391  482 

962067 

92 

640371 

574 

359629 

24 

37 

602728 

481 

962012 

92 

640716 

573 

359284 

23 

38 

603017 

481 

961957 

92 

641060 

573 

358940 

22 

39 

603305 

481 

961902 

92 

641404 

573 

358596 

21 

40 

603594 

480 

961846 

92 

641747 

572 

358253 

20 

41 

9.603882 

480 

9.961791 

92 

9.642091 

572 

10.357909 

19 

42 

604170 

479 

961735 

92 

642434 

572 

357566 

18 

43 

604457 

479 

961680 

92 

642777 

572 

357223 

17 

44 

604745 

479 

961624 

93 

643120 

571 

356880 

16 

45    605032 

478 

961  569  j  93 

643463 

571 

356537 

15 

46    605319 

478 

9615131  93 

643806 

571 

356194 

14 

47 

605606 

478 

961458 

93 

644148 

570 

355852 

13 

48 

605892 

477 

961402 

93 

644490 

570 

355510 

12 

49 

606179   477 

961346  93 

644832 

570 

355168 

11 

50 

606465   476    961290]  93 

645174 

569 

354826 

10 

51 

9.6067MJ  476 

9.  961235!  93 

9.645516 

569 

10.354484 

~9 

52 

6070361  476 

961179 

93 

645857 

569 

354143 

$ 

53 

607322 

475 

961123 

93 

646199 

5G9 

353801 

7 

54 

607607 

475 

961067 

93 

646540 

568 

353460 

6 

55 

607892 

474 

961011 

93 

646881 

568 

353J19 

5 

56 

608177 

474 

960955 

93 

647222 

568 

352778 

4 

57 

608461 

474 

960899 

93 

647562 

5«  7 

352438 

3 

58 

608745 

473 

960843 

94 

647903 

567 

352097 

2 

59 

609029 

473 

960786 

94 

648243 

567 

351757 

1 

60 

609313 

473 

960730 

94 

648583 

566 

351417 

0 

(.'••sine              Sine 

Cnlans.   1 

Tang- 

M. 

4* 


6G  Degic-t 


(24  Degrees.)     A  TABLE  OF  LOGARITHMIC 


M. 

Sine      D.   (  Cosine  |  D. 

Tang.   |   D. 

Cotang. 

0 

9.609313 

473 

9.960730 

94 

9.648583 

566 

10.351417 

60 

1 

6O9597 

472 

960674 

94 

648923 

566 

351077 

59 

2 

609880 

472 

960618 

94 

649263 

566 

350737 

58 

3 

610164 

472 

960561 

94 

649602 

566     350398 

57 

4 

610447 

471 

960505 

94 

649942 

565 

350058 

56 

5 

610729 

471 

960448 

94 

650281 

565 

349719 

55 

6- 

611012 

470 

960392 

94 

650620 

565 

349-380 

54 

7 

611294 

470 

960335 

94 

650959 

564 

349041 

53 

8 

611576 

470 

960279 

94 

651297 

564 

348703 

52 

9 

611858 

469 

960222 

94 

651636 

564 

348364 

51 

10 

612140 

469 

960165 

94 

651974 

563 

348026 

50 

11 

9.612421 

469 

9.960109 

95 

9,652312 

563 

10.347688 

49 

12 

612702 

468 

960052 

95 

652650 

563 

347350 

48 

13 

61  2983   468 

959995 

95 

652988 

563 

347012 

47 

14 

613264   467 

959938 

95 

653326 

562 

346674 

46 

15 

613545 

467 

959882 

95 

653663 

562 

346337 

45 

16 

613825 

467 

959825 

95 

654000 

562 

346000 

44 

17 

614105 

466 

959768 

95 

654337 

561 

345663 

43 

18 

614385 

466 

959711 

95 

654674 

561 

345326 

42 

19 

614665 

466 

959654 

95 

655011 

561 

344989 

41 

20 

614944 

465 

&59S96 

95 

655348 

561 

344652 

40 

21 

9.615223 

465 

9,959539 

95 

9.655684 

560 

10.344316 

39 

22 

615502 

465 

959482 

95 

656020 

560 

343980 

38" 

23 

615781 

464 

959425 

95 

656356 

560 

343644 

37 

24 

616060 

464 

958368 

95 

656692 

559 

343308 

36 

25 

616338 

464 

959310 

96 

657028 

559 

342972 

35 

26 

616616 

463 

959253 

96 

K57364 

559 

342636 

34 

27 

616894 

4S3 

959195 

96 

657699 

559 

342301 

33 

28 

617172 

462 

959138 

96 

658034 

558 

341966 

32 

29 

617450 

462 

959081 

96 

658369 

558 

341631 

31 

30 

617727 

462 

959023 

96 

658704 

558 

341296 

30 

31 

9.618004 

461 

9.958965 

96 

9.659039 

558 

10.340961 

29 

32 

618281 

461 

958908 

96 

659373 

557 

340627 

28 

33 

618558 

461 

958850 

96 

659708 

557 

34029-2 

27 

34 

618834 

460 

958792 

96 

660042 

557 

339958 

26 

35 

619110 

460 

958734 

96 

660376 

557 

339624 

25 

36 

619386 

460 

958677 

96 

660710 

556 

339290 

24 

37 

619G62   459 

958619 

9fi 

661043 

556 

338957 

23 

38 

619938   459 

958561 

96 

661377 

556 

338623 

22 

39 

620213 

459 

958503 

97 

601710   555 

338290 

21 

40 

620488 

458 

958445 

97 

662043   555 

337957 

20 

41 

9.620763!  458 

9  .  958387 

97 

9  662376 

555 

10.337624 

19 

42 

621038   457 

958329 

97 

662709 

554     337291 

18 

43 

621313 

457 

958271!  97 

663042 

554 

336958 

17 

44 

621587 

457 

958213 

97 

663375 

554 

336625 

16 

45 

621861 

456 

958154 

97 

663707 

554 

336293 

15 

46 

622135 

456 

958096 

97 

664039 

553 

335961 

14 

47 

622409 

456 

958038 

97 

664371 

553 

335629 

13 

48 

622682 

455 

957979 

97 

664703 

553 

335297 

12 

49 

622956 

455 

957921 

97 

665035 

553 

334965 

11 

50 

623229 

455 

957863 

97 

665366   552 

334634 

10 

51 

9.6235021  454 

9.957804 

9V 

9.665697 

552 

107334303 

9 

52 

623774!  454 

957746 

98 

666029 

552 

333971 

8 

53 

624047 

454 

957687 

98 

6663601  551 

333640 

7 

54 

624319 

453 

957628 

98 

666691 

551 

333309 

6 

55 

6245911  453 

957570 

98 

667021 

551 

332979 

5 

56 

624863   453 

957511 

98 

667352 

'  551 

332648 

4 

57 

6251351  452 

957452 

98 

667682 

550 

332318 

3 

58 

625406   452 

957393 

98 

668013 

550 

331987 

2 

59 

625677   452 

957335 

98 

668343 

550 

331657 

1 

60 

6259481  451 

957276  98 

668672 

550 

331328 

0 

Cosine           Sine   1    I  Cotang. 

|    Tang.   |  M. 

65  Degrees. 


SINES  AND  TANGENTS.     (26  Degrees.) 


M.  |    Sine     I).     Cosine    D.     Tang.      D.     Cotang.  j 

0 

9.625948 

451 

9.957276 

98  1  9.668673 

550 

10.331327i  60 

1 

626219 

451 

957217 

98'   669002 

549 

330998 

59 

2 

626490 

451 

957158 

98 

669332 

549 

330668 

58 

3 

626760 

450 

957099 

98 

669661 

549 

330339 

57 

4 

627030 

450 

957040 

98 

669991 

548 

330009 

56 

5 

627300 

450 

956981 

98 

670320 

548 

329680 

55 

6 

627570 

449 

956921 

99 

670649 

548 

329351 

54 

7 

627840 

449 

956862 

99 

670977 

548 

329023 

53 

8 

628109 

449 

956803 

99 

671306 

547 

328694 

52 

9 

628378 

448 

956744 

99 

671634 

547 

-  328366 

51 

10 

628647 

448 

956684 

99 

671963 

547 

328037 

50 

11 

9.628916 

447 

9.956625 

99 

9.672291 

547 

10.327709 

49 

12 

629185 

447 

956566 

99 

672619 

546 

327381 

48 

13 

629453 

447 

956506 

99 

672947 

546 

327053 

47 

14 

629721 

446 

956447 

99 

673274 

546 

326726 

46 

15 

629989 

446 

956387 

99 

673602 

546 

326398 

45 

16 

630257 

446 

956327 

99 

673929 

545 

326071 

44 

17 

630524 

446 

956268 

99 

674257 

545 

325743 

43 

18 

630792 

445 

956208 

100 

674584 

545 

325416 

42 

19 

631059 

445 

956148 

100 

674910 

544 

325090 

41 

20 

631326 

445 

956089 

100 

675237 

544 

324763 

40 

21 

9.631593 

444 

9.956029 

100 

9.675564 

544 

10.324436 

39 

22 

631859 

444 

955969 

100 

675890 

544 

324110 

38 

23 

632125 

444  i   955909 

100 

676216 

543 

323784 

37 

24 

632392 

443 

955849 

100 

676543 

543 

323457 

36 

25 

632658 

443 

955789 

100 

676869 

543 

323131 

35 

26 

632923 

443 

955729 

100 

677194 

543 

322806 

34 

27 

633189 

442 

955669 

100 

677520 

542 

322480 

33 

28 

633454 

442 

955609 

100 

677846 

542 

322154 

32 

29 

633719 

442 

955548 

100!   678171 

542 

321829 

31 

30 

633984 

441 

955488 

100 

678496 

542 

321504 

30 

31 

9  .  634249 

441 

9.955428 

101 

9.678821 

541 

10.321179 

29 

32 

634514 

440 

955368 

101 

679146 

54-1 

320854 

28 

33 

634778 

440 

955307 

101 

679471 

541 

320529 

27 

34 

635042 

440 

955247 

101 

679795 

541 

320205 

26 

35 

635306 

439 

955186 

101 

680120 

540 

319880 

25 

36 

63557( 

439 

955126 

101 

680444 

540 

319556 

24 

37 

635834 

439 

955065 

101 

680768 

540 

319232 

23 

38 

636097 

438 

955005 

101 

681092 

540 

318908 

22 

39 

636360 

438 

954944 

101 

681416 

539 

318584 

21 

40 

636623 

438 

954883 

101 

681740 

5Cn 

318260 

20 

41 

9.636886 

437 

9  954823 

10  l!  9.  682063 

539 

10.317937 

19 

42 

637148 

437 

954762 

101 

682387 

539 

317613 

18 

43 

6374111  437 

95470  i 

101 

682710 

538 

317290 

17 

44 

637673 

437 

954640 

101 

683033 

538 

316967 

16 

45 

637935 

436 

954579 

101 

683356 

538 

316644 

15 

46 

638  197 

436 

954518 

102 

683679 

538 

316321 

14 

47 

638458 

436 

954457 

102 

684001 

537 

315999 

13 

48 

63S720 

435 

95439P 

102 

684324 

537 

315676 

12 

49 

638981 

435 

954335 

102 

684646 

537 

315354 

11 

50 

639242 

435 

954274 

102 

684968 

537 

315032 

10 

51 

9.639503 

434 

9.95421o 

102 

9.685290 

536 

10.314710 

9 

52 

639764 

434 

954152 

102  f   685612 

536 

314388 

8 

53 

640024 

434 

954090 

102 

685934 

536 

314066 

1 

54 

640284 

433 

954029 

102 

686255 

536 

313745 

( 

55 

640544 

433 

953968 

102 

68657? 

C35 

313423 

56 

640804 

433 

95390 

102 

686898 

535 

313102 

57 

641064 

432 

95384 

102 

687219 

535 

312781 

[ 

58 

641324 

432 

95378. 

102 

687540   535 

312461 

< 

59 

641584 

-   432 

95372' 

103 

6878611  534 

31213! 

60 

64184$ 

431  i   95366C 

103   6881821  534 

31181S 

1   Cosine 

Sine 

Cotang. 

Tang.   j  M. 

64  Degrets. 


44 


Degrees.;     A  TABLE  OF  LOGARITHMIC 


M.    Sine     D.     Cosine   |  D.  |   Tane. 

D,     Cotang. 

0 

9.641842 

431 

9.953660 

103 

9.688182 

534 

10.311818 

60 

1 

642101 

431 

953599 

103 

688502 

534 

311498 

59 

2 

642360 

431 

953537 

103 

688823 

534 

311177 

58 

3 

642618 

430 

953475 

103 

689143 

533 

310857 

57 

4 

642877 

430 

953413 

103 

689463 

533 

310537 

56 

5 

643135 

430 

953352 

103 

689783 

533 

310217 

55 

6 

643393 

430 

953290 

103 

690103 

533 

309897 

54 

7 

643650 

429 

953228 

103 

690423 

533 

309577 

53 

8 

643908   429 

953166 

103 

690742 

532 

309258 

52 

9 

644165 

429 

953104 

103 

691062 

532 

308938 

51 

10 

644423 

428 

953042 

103 

691381 

532 

308619 

50 

11 

9.644680   428 

9.952980 

104 

9.691700 

531 

10.308300 

49 

12 

644936  |  428 

952918 

104 

692019 

531 

307981 

48 

13 

645193   427 

952855 

104 

692338 

531 

307662 

47 

14 

645450 

427 

952793 

104 

692656 

531 

307344 

46 

15 

645706 

427 

952731 

104 

692975 

531 

307025- 

45 

16 

645962 

426 

952669 

104 

693293 

530 

306707 

44 

17 

646218 

426 

952606 

104 

693612 

530 

306388 

43 

18 

646474 

426 

952544 

1041   693930 

530 

306070 

42 

19 

646729 

425 

952481 

104 

694248 

530 

305752 

41 

20 

646984 

425 

952419 

104 

694566 

529 

305434 

40 

21 

9.647240 

425 

9.952356 

104 

9  .  694883 

529 

10.3'05117 

39 

22 

647494 

424 

952294 

104 

695201 

529 

304799 

38 

23 

647749 

424 

952231 

104 

695518 

529 

304482 

37 

24 

648004 

424 

952168 

105 

695836 

529 

304164 

36 

35 

648258 

424 

952106 

105 

696153 

528 

303847 

35 

26 

648512 

423 

952043 

105 

696470 

528 

303530 

34 

27 

648766 

423 

951980 

105 

696787 

528 

303213 

33 

28 

649020 

423 

951917 

105 

697103 

528 

302897 

32 

29 

649274 

422 

951854 

105  i   697420 

527 

302580 

31 

30 

649527 

422 

951791 

105 

697736 

527 

302264 

30 

31 

9.649781 

422 

9.951728 

105  ST.  698053 

527 

10.301947 

29 

32 

650034 

422 

951665 

105 

698369|  527 

301631 

28 

33 

650287 

421 

951602 

105 

698685 

526 

301315 

27 

34 

650539 

421 

951539 

105   699001 

526 

300999 

26 

35 

650792 

421 

951476 

105!   699316 

526 

300684 

25 

36 

651044 

420 

951412 

105   699632 

526 

300368 

24 

37 

651297 

420 

951349 

1061   699947 

526 

300053 

23 

38 

651549 

420 

951286 

106   700263 

525 

299737 

22 

39 

651800 

419 

951222 

106   700578 

525 

299422 

21 

40 

652052 

419 

951159 

106   700893)  525 

299107 

20 

41 

9.652304 

419 

9.951096 

106  9.701208 

524 

10.298792 

19 

42 

652555 

418 

951032 

106   701523 

524 

298477 

18 

43 

652806 

418 

950968 

106   701837   524 

298163 

17 

44 

653057 

418 

950905 

106   702152   524 

297848 

16 

45 

653308 

418 

950841 

106   702466   524 

297534 

15 

46 

653558 

417 

950778 

106^   702780   523 

297220 

14 

47 

653808 

417 

950714 

106|   703095   523 

296905 

13 

48 

654059 

417 

950650 

106'   703409:  523 

296591 

12 

49 

654309 

416 

950586 

106   7037231  523 

296277 

11 

50 

654558 

416 

950522 

107   704036!  522 

295964 

10 

51 

9.654808 

416 

9.950458 

1079.704350   522 

10.295650 

9 

52 

655058 

416 

950394 

107   704663;  522 

295337 

8 

53 

6553071  415 

950330 

107;   704977^  522 

295023 

? 

54 

6555561  415 

950266 

107   705290   522 

294710 

6 

55 

655805:  415 

950202 

107   705603   521 

294397 

5 

56 

656054i  414 

950138 

107!   705916   521 

294084 

4 

57 

656302!  414 

950074 

107   706228'  521 

293772 

3 

58 

656551!  414 

950010 

107,   706541 

521 

293459 

2 

59 

656799   413 

949345 

107,   706854 

521 

293146 

1 

60 

6570471  413 

949881 

107i   707166 

520 

292834 

0 

|   Cosine  I 

Sine   |    |   Ootang.  | 

Tang.     M. 

C3  Decrees. 


SINES  ANP  TANGENTS. 


Degrees.) 


45 


M 

Sine   |  .  I)   |  Cosine    D  |   Tang.   |   D.     Cotang.   | 

0 

9.657047 

413 

9.949881 

J07 

9.707166 

520 

10.292834 

60 

657295 

413 

949816 

107 

707478 

520 

292522 

59 

2 

657542 

412 

949752 

107 

707790 

520 

292210 

58 

3 

657790 

412 

949688 

108 

708102 

520 

291898 

57 

4 

658037 

412 

949623 

108 

708414 

519 

291586 

56 

5 

658284 

412 

949558 

108 

708726 

519 

291274 

55 

6 

658531 

411 

949494 

108 

709037 

519 

290963 

54 

7 

658778 

411 

949429 

108 

709349 

519 

290651 

53 

8 

659025 

411 

949364 

108 

709660 

519 

290340 

52 

9 

659271 

410 

949300 

108 

709971 

518 

290029 

51 

10 

659517 

410 

949235 

108 

710282 

518 

289718 

50 

11 

9.659763 

410 

9.949170 

108 

9.710593 

518 

10.289407 

49 

12 

660009 

409 

949105 

108 

710904 

518 

289096 

48 

13 

660255 

409 

949040 

108 

711215 

518 

288785 

47 

14 

660501 

409 

948975 

108 

711525 

517 

288475 

46 

15 

660746 

409 

948910 

108 

711836 

517 

288164 

45 

16 

660991 

408 

948845 

108 

712146 

517 

287854 

44 

17 

661236 

408 

948780 

109 

712456 

517 

287544 

43 

18 

661481 

408 

948715 

109 

712766 

516 

287234 

42 

19 

661726 

407 

948650 

109 

713076 

516 

286924 

41 

20 

661970 

407 

948584 

109 

713386 

516 

286614 

40 

21 

9.662214 

407 

9.948519 

1Q9 

9.713696 

516 

10.286304 

39 

22 

662459 

407 

948454 

109 

714005 

516 

285995 

38 

23 

662703 

406 

948388 

109 

714314 

515 

285686 

37 

24 

662946 

406 

948323 

109 

714624 

515 

285376 

36 

25 

663190 

406 

948257 

109 

714933 

515 

28506? 

35 

26 

663433 

405 

948192 

109 

715242 

515 

284758 

34 

27 

663677 

405 

948126 

109 

715551 

514 

284449 

33 

28 

663920 

405 

948060 

109 

715860 

514 

284140 

32 

29 

'664163 

405 

947995 

110 

716168 

514 

283832 

31 

30 

664406 

404 

947929 

110 

716477 

514 

283523 

30 

31 

9.664648 

404 

9.947863 

no 

9.716785 

514 

10.283215 

29 

32 

664891 

404 

947797 

110 

717093 

513 

282907 

28 

33 

665133 

403 

947731 

110 

717401 

513 

282599 

27 

34 

665375 

403 

947665 

110 

717709 

513 

282291 

26 

35 

665617 

403 

947600 

110 

718017 

513 

281983 

25 

36 

665859 

402 

947533 

110 

718325 

513 

281675 

24 

37 

666100 

402 

947467 

110 

718633 

512 

281367 

23 

38 

666342 

402 

947401 

110 

718940 

512 

281060 

22 

39 

666583 

402 

947335 

110 

719248 

512 

280752 

21 

40 

666824 

401 

947269 

110 

719555 

512 

280445 

20 

41 

9.667065 

401 

9.947203 

110 

9.719862 

512 

10.280138 

19 

42 

667305 

401 

947136 

111 

720169 

511 

279831 

18 

43 

667546 

401 

947070 

111 

720476 

511 

279524 

17 

44 

'  667786 

400 

947004 

111 

720783 

511 

279217 

16 

45 

668027 

400 

946937 

111 

721089 

511 

278911 

15 

46 

668267 

400 

946871 

111 

721396 

511 

278604 

14 

47 

668506 

399 

946804 

111 

721702 

510 

278298 

13 

48 

668746 

399 

946738 

111 

722009 

510 

277991 

12 

49 

668986 

399 

946671 

111 

722315 

510 

277685 

11 

50 

669225 

399 

946604 

111 

722621 

510 

277379 

10 

51 

9.669464 

398 

9.946538 

111 

9.722927 

510 

10.277073 

9 

52 

669703 

398 

946471 

111 

723232 

509 

276768 

8 

53 

669942 

398 

946404 

111 

723538 

509 

276462 

7 

54 

670181 

397 

946337 

111 

723844 

509 

276156 

6 

55 

670419 

397 

946270 

112 

724149 

509 

275851 

5 

56 

670658 

397 

946203 

112 

724454 

509 

275546 

4 

57 

670896 

397 

946136 

112 

724759 

508 

275241 

3 

58 

671134 

396 

946069 

112 

725065 

508 

274935 

2 

59 

671372 

396 

946002 

112 

725369 

508 

274631 

1 

60 

671609 

396 

945935 

112 

725674 

508 

274326 

0 

Cosine 

Sine    | 

Cotang. 

|    Tang.  |  M. 

62  Degrees. 


46 


(28  Degrees. )     A  TABLE  OP  LOGARITHMIC 


M.     Sine   |   D.   1   Conine   |  D.  |   Tane.      H.   |   Cotans.   | 

0 

9.67160S 

396 

9.945935 

112 

9.725674 

508  1  10.274323 

60 

1 

671847 

395 

945868 

112 

725979 

508  1    274021 

59 

2 

672084 

395 

945800 

112 

726284 

507 

273716 

58 

3 

672321 

395 

945733 

112 

726588 

507 

273412 

57 

4 

672558 

395 

945666 

112 

726892 

507 

273108 

56 

5 

672795 

394 

945598 

112 

727197 

507 

272803 

55 

6 

673032 

394 

945531 

112 

727501 

507 

272499 

54 

7 

673268 

304 

945464 

113 

727805 

506 

272195 

53 

8 

673505 

394 

945396 

113 

728109 

506 

271891 

52 

9 

673741 

393 

945328 

113 

728412 

506 

271588 

51 

10 

673977 

393 

945261 

113 

728716 

506 

271284 

50 

11 

9.674213 

393 

9.945193 

113 

9.729020 

506 

10.270980 

49 

12 

674448 

392 

945125 

113 

729323 

505 

270677 

48 

13 

674684 

392 

945058 

113 

729626 

505 

270374 

47 

14 

674919 

392 

944990  113 

729929 

'  505 

270071 

46 

15 

675155 

392 

944922 

113 

730233 

505 

269767 

45 

16 

675390 

391 

944854 

113 

730535 

505 

269465 

44 

17 

675624 

391 

944786 

113 

730838 

504 

269162 

43 

18 

675859 

391 

944718 

113 

731141 

504 

268859 

42 

19 

676094 

391 

944650 

113 

731444 

504 

268556 

41 

20 

676328 

390 

944582 

114 

731746 

504 

268254 

40 

21 

9.676562 

390 

9.944514 

114 

9.732048 

504 

10.267952 

39 

22 

676796 

390 

944446 

114 

732351 

503 

267649 

38 

23 

677030 

390 

944377 

114 

732653 

503 

267347 

37 

24 

677264 

389 

944309 

114 

732955 

503 

267045 

36 

25 

677498 

389 

944241 

114 

733257 

503 

266743 

35 

26 

677731 

389 

944  172 

114 

733558 

503 

266442 

34 

27 

677964 

388 

944104  114 

733860 

502 

266140 

33 

28 

678197 

388 

944036 

114 

734162 

502 

265838 

32 

29 

678430 

388 

943967 

114 

734463 

502 

265537 

31 

30 

678683 

388 

943899 

114 

734764 

502 

265236 

30 

31 

9  678895 

387 

9  .  943830 

114 

9.735066 

502 

107264934 

29 

32 

679128 

387 

943761 

114 

735367 

502 

264633 

28 

33 

679360 

387 

943693 

115 

735668 

501 

264332 

27 

34 

679592 

387 

943624 

115 

735969 

501 

264031 

26 

35 

679824 

386 

943555 

115 

736269 

501 

263731 

25 

36 

680056 

386 

943486 

115 

736570 

501 

263430 

24 

37 

680288 

386 

943417 

115 

736871 

501 

263129 

23 

38 

680519 

385 

943348 

115 

737171 

500 

262829 

22 

39 

680750 

385 

943279 

115 

737471 

500 

262529 

21 

40 

680982 

385 

943210 

115 

737771 

500 

262229 

20 

41 

9.681213 

385 

9.943141 

US 

9.  '738071 

500 

10.261929 

19 

42 

681443 

384 

943072 

115 

738371 

500 

261629 

18 

43 

681674 

384 

943003 

115 

738671 

499 

261329 

17 

44 

681905 

384 

942934 

115 

738971 

499 

261029 

16 

45 

682135 

384 

942864 

115 

739271 

499 

260729 

15 

46 

682365 

383 

942795  116 

739570 

499 

260430 

14 

47 

682595 

383 

942726 

116 

739870 

499 

260130 

13 

48 

682825 

383 

942656 

116 

740169 

499 

259831 

12 

49 

683055 

383 

942587 

116 

740468 

498 

259532 

11 

50 

683284 

382 

942517 

116 

740767 

498 

259233 

10 

51 

9.683514 

382 

9.942448 

116 

9.741066 

498 

10.258934 

~9 

o2 

683743 

382 

942378 

116 

741365 

498 

258635 

8 

53 

683972 

382 

942308 

116 

741664 

498 

258336 

7 

54 

684201 

381 

942239 

116 

741962 

497 

258038 

6 

55 

684430 

381 

942169 

116 

742261 

497 

257739 

5 

56 

684658 

381 

942099 

116 

742559 

497 

257441 

4 

57 

684887 

380 

942029 

116 

742858 

497 

257142 

3 

58 

685115 

380 

941959 

116 

743156 

497 

256844 

2 

59 

655343 

380 

941889 

117 

743454 

497 

256546 

1 

60 

685571 

380 

941819 

117 

743752 

496 

256248 

0 

Cosine 

|   Sinn 

|  Cotang.  | 

Tang.   )  M. 

61  Degrees, 


SINES  AND  TANGENTS.      ^29  Degrees.; 


47 


M.  |   Sine   |   D.    Cosine   |  D. 

Tang.   (   D.   |   Cotarig. 

0 

9.685571 

380 

9.941819  117 

9.743752 

496 

10.256248 

60 

1 

685799 

379 

941749 

117 

744050 

496 

255950 

59 

2 

686027 

379 

941679 

117 

744348 

496 

255652 

58 

3 

686254 

379 

941609 

117 

744645 

496 

255355 

57 

4 

686482 

379 

941539 

117 

744943 

496 

•255057 

56 

5 

686709 

378 

941469 

117 

745240 

•496 

254760 

55 

6 

686936 

378 

941398 

117 

745538 

495 

254462 

54 

7 

687163 

378 

941328 

117 

745835 

495 

254165 

53 

8 

6S7389 

378 

941258 

117 

746132 

495 

253868 

52 

9 

687616 

377 

941187 

117 

746429 

495 

253571 

51 

10 

687843 

377 

941117 

117 

746726 

'495 

253274 

50 

11 

9.688069 

377 

9.941046 

118 

9.747023 

494 

10.252977 

49 

12 

688295 

377 

940975 

118 

747319 

494 

252681 

48 

13 

688521 

376 

940905 

118 

747616 

494 

252384 

47 

14 

688747 

376 

940834 

118 

747913 

494 

252087 

46 

15 

688972 

376 

940763 

118 

748209 

x494 

251791 

45 

16 

689198 

376 

940693 

118 

748505 

493 

251495 

44 

17 

689423 

375 

940622 

118 

748801 

493 

251199 

43 

18 

689648 

375 

94Q551 

118 

749097 

493 

250903 

42 

19 

689873   375 

940480 

118 

749393 

493 

'  250607 

41 

20 

690098   375 

940409 

118 

7496P9 

493 

250311 

40 

21 

9.6903231  374 

9.940338 

118 

9  .  749985 

493 

10T250015 

39 

22 

690548)  374 

940267 

118 

750281 

492 

249719 

38 

23 

690772!  374 

940196 

118 

750576 

492 

249424 

37 

24 

690996   374 

940125 

119 

750872 

492 

249128 

36 

25 

691220   373 

940054 

119 

751167 

492 

248833 

35 

26 

691444|  373 

939982 

119 

751462 

492 

248538 

34 

27 

6916681  373 

939911 

119 

751757 

492 

248243 

33 

28 

691892   373 

939840 

119 

752052 

491 

247948 

32 

29 

692115   372 

939768 

119 

752347 

491 

247653 

31 

30 

692339!  372 

939697 

113 

752642 

491 

247358 

.30 

31 

9  .  692562   372 

9.939625 

119 

9  .  752937 

491 

10.247063 

29 

32 

692785   371 

939554 

119 

753231 

491 

246769 

28 

33 

693008 

371 

939482 

119 

753526 

491 

246474 

27 

34 

693231 

371 

939410 

119 

753820 

490 

246180 

26 

35 

693453   371 

939339 

119 

754115 

490 

245885 

25 

36 

693676 

370 

939267 

120 

754409 

490 

24559  1 

24 

37 

693898 

370 

939195 

120 

754703   490 

245297 

23 

38 

694120 

370 

939123 

120 

754997 

490 

245003 

22 

39 

694342   370 

939052 

120 

75529  1 

490 

244709 

21 

40 

694504   369 

93S980 

120   755585 

489 

244415 

20 

41 

9  .  694786   369 

9.938908 

120 

9  .  755878 

489 

10.244122!  19 

42 

695007;  36«) 

938836 

120 

756172 

489 

2438281  18 

43 

695229!  369 

938763 

120 

756465   489 

243535 

17 

44 

6954501  368 

938691 

120 

756759 

489 

243241 

16 

45 
46 

695671   368 
6958921   368 

938619:  120 
936547  120 

757052 
757345 

489 

488 

242948 
242655 

15 

14 

47 

696113   368 

938475  120   757638 

488 

242362 

13 

48 

696334   367 

938402!  121 

757931 

488 

242069 

12 

49 

696f>54:   367 

938330!  121 

758224 

488 

241776 

11 

50 

696775   367 

938258!  121 

758517 

488 

241483 

10 

51 

9.696926  367 

9.938185'  T2Ti  9.758810 

488" 

107241  190 

Q 

52 

697215   366 

938113  121   759102 

487 

240898 

w 

53 

697435   366 

938040!  121 

759395 

487 

240605 

7 

54 

697654   366 

937967  121 

759687 

487 

240313 

6 

55 

697874   366 

9378951  121 

759979 

487 

240021 

5 

56 

693094   365 

937822  121 

760272 

487 

239728 

4 

57 

698313:   365 

937749  121 

760564 

487 

239436 

3 

58 

698531 

5   365 

937676  121 

760856 

486 

239144 

2 

59 

69875  J 

365 

937604  121 

761148 

486 

238852 

1 

60 

69897( 

)   364 

937531!  121   761439 

486 

238561 

0 

Cosine   J       |   Sine   |      Cotaiig.   |          Tang   j  M- 

GO  Degrees 


48 


(30  Degrees.)     A  TABLE  OF  LOGARITHMIC 


M.  |   Sine   |   D.   |  Cosine   |  D.    Tang.   |   [).   |   Cotnng. 

0 

9.698970 

364 

9.937531 

121 

9.761439 

486 

10.238561 

60 

1 

699189 

364 

937458 

122 

761731 

486 

238269 

59 

2 

699407 

364 

937385 

122 

762023 

486 

237977 

58 

3 

699626 

364 

937312 

122 

762314 

486 

237686 

57 

4 

699844 

363 

937238 

122 

762606 

485 

237394 

56, 

5 

700062 

363 

9371.65 

122 

762897 

485 

237103 

55: 

6 

700280 

363 

937092 

122 

763188 

485 

236812 

541 

7 

700498 

363 

937019 

122 

763479 

485 

236521 

53 

8 

700716 

363 

936946 

122 

763770 

485 

236230 

52 

9 

700933 

362 

936872 

122 

764061 

485 

235939 

51 

10 

701151 

362 

936799 

122 

764352 

484 

235648 

50 

11 

9.701368 

362 

9.936725 

122 

9.764643 

484 

10.235357 

49 

12 

701585 

362 

936652 

123 

764933 

484 

235067 

48 

13 

701802 

361 

936578 

123 

765224 

484 

234776 

47 

14 

702019 

361 

936505 

123 

7655141  484 

234486 

46 

15 

702236 

361 

936431 

123 

765805 

484 

234195 

45 

16 

702452 

361 

936357 

123 

766095 

484 

233905 

44 

17 

702669 

360 

936284 

123 

766385 

483 

233615 

43 

18 

702885 

360 

936210 

123 

766675 

483 

233325 

42 

19 

703101 

360 

936136 

123 

766965 

483 

233035 

41 

20 

703317 

360 

936062 

123 

767255 

483 

232745 

40 

21 

9.703533 

359 

9.935988 

123 

9.767545 

483 

10.232455 

39 

22 

703749 

359 

935914 

123 

767834 

483 

232166 

38 

23 

703964 

359 

935840 

123 

768124 

482 

231876 

37 

24 

704179 

359 

935766 

124 

768413 

482 

231587 

36 

25 

704395 

359 

935692 

124 

768703 

482 

231297 

35 

26 

704610 

358 

935618 

124 

768992 

482 

231008 

34 

27 

704825 

358 

935543 

124 

769281 

482 

230719 

33 

28 

705040 

358 

935469 

124 

769570 

482 

230430 

32 

29 

705254 

358 

935395 

124 

769860 

481 

230140 

31 

30 

705469 

357 

935320 

124 

770148 

481 

229852 

30 

31 

9.705683 

357 

9.935246 

124 

9.770437 

481 

10.229563 

29 

32 

705898 

357 

935171 

124 

770726 

481 

229274 

28 

33 

706112 

357 

935097 

124 

771015 

481 

228985 

27 

34 

706326 

356 

935022 

124 

771303 

481 

228697 

26 

35 

706539 

356 

9349431  124 

771592 

481 

228408 

25 

36 

706753 

356 

934873 

124!   771880 

480 

228120 

24 

37 

706967 

356 

934798 

125 

772168 

480 

227832 

23 

38 

707180 

355 

934723 

125 

772457 

480 

227543 

22 

39 

707393 

355 

934649 

125 

772745 

480 

227255 

21 

40 

707606 

355 

934574 

125 

773033 

480 

226967 

20 

41 

9.707819 

355 

9  .  934499 

125 

9  .  77332  1 

480 

10.226679 

19 

42 

708032 

354 

934424 

125 

773608 

479 

226392 

18 

43 

708245 

354 

934349 

125 

773896 

479 

226104 

17 

44 

708458   354 

934274 

125 

774184 

479 

225816 

16 

45 

708670   354 

934199 

125 

774471 

479 

225529 

15 

46 

708882 

353 

934123 

I2.r» 

774759 

479 

225241 

14 

47 

709094 

353 

9X1048  125 

775040 

479 

224954 

13 

48 

709306 

353 

9339731  125 

775333 

479 

224667 

12 

49 

709518 

353 

933898 

126 

775621 

478 

224379 

11 

50 

709730 

353 

933822 

126 

775908 

478 

224092 

10 

51 

9  709941 

352 

9.933747 

126 

9.776195 

478 

10.223805 

9 

52 

710153 

352 

933671 

1261   776482 

478 

223518 

8 

53 

710364 

352 

933596 

126 

776769 

478 

223231 

7 

54 

710575 

'  352 

933520 

126 

777055 

478 

222945 

6 

55 

710786 

351 

933445 

126 

777342 

478 

222658 

5 

56 

710997 

351 

933369 

126 

777628 

477 

222372 

4 

57 

711208 

351 

933293 

126 

777913 

477 

222085 

3 

58 

711419 

351 

933217 

126 

778201 

477 

221799 

2 

59 

711629 

350 

933141 

126 

778487 

477 

221512 

1 

60 

711839 

350 

933066 

126 

778774 

477 

221226 

0 

Cosine             Sine   |       Cutanj;.   1           Tang.   1  M. 

59  Uc^i 


SINES  AND  TANGENTS.      (31  Degrees.) 


M.  |   Sine 

D.  |   Cosine    D.  |   Taiip.     D.     Cotang. 

0 

9  711839 

350 

9.933066 

126 

9.778774 

477 

10.221226160 

1 

'  712050 

350 

932990 

127 

779060 

477 

220940 

59 

o 

712260 

350 

932914 

127 

779346 

176 

220654 

58 

3 

712469 

349 

932838 

127 

779632 

476 

220368 

57 

4 

712679 

349 

932762 

127 

779918   476 

220082 

56 

5 

712889 

349 

932685 

127 

780203;  476 

219797 

55 

6 

713098 

349 

932609 

127 

780489   476 

219511 

54 

7 

713308 

349 

932533 

127 

780775   476 

219225 

53 

8 

713517 

348 

932457 

127 

781060!  476 

218940 

52 

9 

713726 

348 

932380 

127 

781346 

475 

218654 

51 

10 

713935 

348 

932304 

]27 

781631 

475 

218369 

50 

11 

9.714144 

348 

9.932228 

127 

9.781916 

475 

10.218084 

49 

12 

*  714352 

347 

932151 

127 

782201 

475 

217799 

48 

13 

714561 

347 

932075 

128 

782486 

475 

217514 

47 

14 

714769 

347 

931998 

128 

782771 

475 

217229 

46 

15 

714978 

347 

931921 

128 

783056 

475 

216944 

45 

16 

715186 

347 

931845 

12S 

783341 

475 

216659 

44 

17 

715394 

346 

931768 

128 

783626 

474 

216374 

43 

18 

715602 

346 

931691 

128 

783910   474 

216090 

42 

19 

715809 

346 

931614 

128 

784195   474 

215805 

41 

20 

716017 

346 

931537 

128 

784479   474 

215521 

40 

21 

9.716224 

345 

9.931460 

128 

9.7847641  474 

10.215236 

39 

22 

716432 

345 

931383 

128 

785048   474 

214952 

38 

23 

716639 

345 

931306 

128 

785332 

473 

214668 

37 

24 

716846 

345 

931229 

129 

785616 

473 

214384 

36 

25 

717053 

345 

931152 

129 

785900 

473 

214100 

35 

26  1   717259 

344 

931075 

129 

786184 

473 

213816 

34 

27 

717466 

344 

930998 

129 

786468   473 

213532 

33 

2S 

717673 

344 

930921 

129 

786752 

473 

213248 

32 

29 

717879 

344 

930843 

129 

787036 

473 

212964 

31 

30 

718085 

343 

930766 

129 

787319 

472 

212681 

30 

31 

9.718291 

343 

9.930688 

129 

9.787603 

472 

10.212397 

29 

32 

718497 

343 

930611 

129 

787886 

472 

212114 

28 

33 

718703 

343 

930533 

129 

788170 

472 

211830 

27 

34 

718909 

343 

930456 

129 

788453 

472 

211547 

26 

35 

719114 

342 

930378 

129 

788736 

472 

211264 

25 

36 

719320 

342 

930300 

130 

789019 

472 

210981 

24 

37 

719525 

342 

930223 

130 

789302 

471 

210698 

23 

38 

719730 

342 

930145 

130 

789585 

471 

210415 

22 

39 

719935 

341 

930067 

130 

789868 

471 

210132 

21 

40 

720140 

341 

929989 

130 

790151 

471 

209849 

20 

41 

9  .  720345 

341 

9.929911 

130 

9.790433 

471 

10.209567 

19 

42 

720549 

341 

929833 

130 

790716 

471 

209284 

18 

43 

720754 

340 

929755 

130 

790999 

471 

209001 

17 

44 

720958 

340 

929677 

130 

791281 

471 

208719 

16 

45 

721162 

340 

929599 

130 

791563 

470 

208437 

15 

46 

721366 

340 

929521 

130 

791846 

470 

208154 

14 

47 

721570 

340 

929442 

130 

792128 

470 

207872 

13 

48 

721774 

339 

929364 

131 

792410 

470 

207590 

12 

49 

721978 

339 

929286 

131 

792692 

470 

207308 

11 

50 

722181   339 

929207 

131 

792974 

470 

207026 

10 

51 

9  .  722385 

339 

9.929129 

131 

9.793256 

470  10.206744 

9 

52 

722588 

339 

929050 

131 

793538 

469 

206462 

8 

53 

722791 

338 

928972 

131 

793819 

469  j    206181 

7 

54 

722994 

338 

928893 

131 

794101 

469 

205899 

6 

55 

723197 

338 

928815 

131 

794383 

469 

205617 

5 

56 

723400 

338 

928736 

131 

794664   469 

205336 

4 

57 

723603 

337 

928657 

131 

794945   469 

205055 

3 

58 

723805 

337 

928578 

131 

795227 

469 

204773 

2 

59 

724007 

337 

928499 

131 

795508 

468 

204492 

1 

60 

724210 

337 

928420 

131 

7957891  468 

204211 

0 

Cosine         |   Sine   |       Cotang.  j      |   Tang.    M. 

58  Degrees. 


50 


(32  Degrees.;     A  TABLE  or  LOOAEITHMIC 


W.    Sine   |   D.     Cosine   |  D.  |   Tang. 

D. 

Cotang.  | 

0 

9.724210 

337 

9  .  928420 

132 

9.795789 

468 

10.204211 

60 

1 

724412 

337 

928342 

132 

796070 

468 

203930 

59 

2 

724614 

336 

928263 

132 

796351 

468 

203649 

58 

3 

724816 

336 

928183 

132 

796632 

468 

203368 

57 

4 

725017 

336 

928104 

132 

796913 

468 

203087 

56 

5 

725219 

336 

928025 

132 

797194 

468 

202806 

55 

6 

725420 

335 

927946 

132 

797475 

468 

202525 

54 

7 

725622 

335 

•927867 

132 

797755 

468 

202245 

53 

8 

725823 

335 

927787 

132 

798036 

467 

201964 

52 

9 

726024 

335 

927708 

132 

798316 

467 

201684 

51 

10 

726225 

335 

927629 

132 

798596 

467 

201404 

50 

11 

9.726426 

334 

9.927549 

132 

9  .  798877 

467 

10.201123 

49 

12 

726626 

334 

927470 

133 

799157 

467 

200843 

48 

13 

726827 

334 

927390 

133 

799437 

467 

200563 

47 

14 

727027 

334 

927310 

133 

799717 

467 

200283 

46 

15 

727228 

334 

927231 

133 

799997 

466 

200003 

45 

16 

727428 

333 

927151 

133 

800277 

466 

199723 

44 

17 

727628 

333 

927071 

133 

800557 

466 

199443 

43 

18 

727828 

333 

926991 

133 

800836 

466 

199164 

42 

19 

728027 

333 

926911 

133 

801116 

466 

198884 

41 

20 

728227 

333 

926831 

133 

801396 

466 

198604 

40 

21 

9.72842? 

332 

9.926751 

133 

9.801675 

466 

10.198325 

39 

22 

728626 

332 

926671 

133 

801955 

466 

198045 

38 

23 

728825 

332 

926591 

133 

802234 

465 

197766 

37 

24 

729024 

332 

926511 

134 

802513 

465 

197487 

36 

25 

729223 

331 

926431 

134 

802792 

465 

197208 

35 

26 

729422 

331 

926351 

134 

803072 

465 

196928 

34 

27 

729621 

331 

926270 

134 

803351 

465 

196649 

33 

28 

729820 

331 

926190 

134 

803630 

465 

196370 

32 

29 

730018 

330 

926110 

134 

803908 

465 

196092 

31 

30 

730216 

330 

926029 

134 

804187 

465 

195813 

30 

31 

9.730415 

330 

9.925949 

134 

9.804466 

464 

10.195534 

29 

32 

730613 

330 

925868 

134 

804745 

464 

195255 

28 

33 

730811 

330 

925788 

134 

805023 

464 

194977 

27 

34 

731009 

329 

925707 

134 

805302 

464 

194698 

26 

35 

731206 

329 

925626 

134 

805580 

464 

194420 

25 

36 

731404 

329 

925545 

135 

805859 

464 

194141 

24 

37 

731602 

329 

925465 

135 

806137 

464 

193863 

23 

38 

731799 

329 

925384 

135 

806415 

463 

193585 

22 

39 

731996 

328 

925303 

135 

806693 

463 

193307 

21 

40 

732193 

328 

925222 

135 

806971 

463 

193029 

20 

41 

9.732390 

328 

9.925141 

135 

9.807249 

463 

10.192751 

19 

42 

732587 

328 

"  925060 

135 

807527 

463 

192473 

18 

43 

732784 

328 

924979 

135 

807805 

463 

192195 

17 

44 

732980 

327 

924897 

135 

808083 

463 

191917 

16 

45 

733177 

327 

924816 

135 

808361 

463 

191639 

15 

46 

733373 

327 

924735 

136 

808638 

462 

191362 

14 

47 

733569 

327 

924654 

136 

808916 

462 

191084 

13 

48 

733765 

327 

924572 

136 

809193 

462 

190807 

12 

49 

733961 

326 

924491 

136 

809471 

462 

190529 

11 

50 

734157 

326 

924409 

136 

809748 

462 

190252 

10 

51 

9.734353 

326 

9.924328 

136 

9.810025 

462 

10.189975  9 

52 

734549 

320 

924246 

136 

810302 

462 

189698 

8 

53 

734744 

325 

924164 

136 

810580 

462 

189420 

7 

54 

734939 

325 

924083 

136 

810857 

462 

189143 

6 

55 

735135 

325 

924001 

136 

811134 

461 

188866 

5 

56 

735330 

325 

923919 

136 

811410 

461 

188590 

4 

57 

735525 

325 

923837 

136 

811687 

461 

188313 

3 

58 

735719 

324 

923755 

137 

811964 

461 

188036 

2 

59 

735914 

324 

923673 

137 

812241 

461 

187759 

1 

60 

736109 

324 

92H591 

137 

818517 

461 

187483 

0 

|  Cosine   j 

Sine 

|   Cotang. 

Tang. 

M. 

57  Degrees. 


SINES  AND  TANGENTS.     (^33  Degrees.) 


51 


M. 

Sine   |   J).     Cosine    1).  \   T;uig.      D.      Cotai^.  | 

0 

9.736109 

324 

9.923591 

137 

9  .  8  1  25  1  7 

461 

10.  187482|  60 

1 

736303 

324 

923509 

137 

812794 

461 

187206 

59 

2 

736498 

324 

923427 

137 

813070 

461 

186930 

58 

3 

738S92 

323 

923345 

137 

813347 

460 

186653 

57 

4 

736880 

323 

923263 

137 

813623 

460 

186377 

56 

fi 

737080 

323 

923181 

137 

813899 

460 

186101 

55 

6 

737274 

323 

923098 

137 

814175 

460 

185825 

54 

7 

737467 

323 

923016 

137 

814452 

460 

185548 

53 

8 

737661 

322 

922933 

137 

814728 

460 

185272 

52 

9 

737855 

322 

922851 

137 

815004 

4<30 

184996 

51 

10 

738048 

322 

922768 

138 

815279 

460 

184721 

50 

11 

9.738241 

322 

9.922686 

13S 

9.815555 

459 

10.184445 

49 

12 

738434 

322 

922603 

138 

815831 

459 

184169 

48 

13 

738627 

321 

922520 

138 

816107 

459 

183893 

47 

14 

738820 

321 

922438 

138 

816382 

459 

183618 

46 

15 

739013 

321 

922355 

138 

816658 

459 

183342 

45 

16 

739206 

321 

922272 

138 

816933 

459 

183067 

44 

17 

739398 

321 

922189 

138 

817209 

459 

182791 

43 

18 

739590 

320 

922106 

138 

817484 

459 

182516 

42 

19 

739783 

320 

922023 

138 

817759 

459 

182241 

41 

20 

739975 

320 

921940 

138 

818035 

458 

181965 

40 

21 

9.740167 

3:20 

9.921857 

139 

9.818310 

458 

10.181690 

39 

22 

740359 

320 

921774 

139 

818585 

458 

181415 

38 

23 

740550 

319 

921691 

139 

818860 

458 

181140 

37 

24 

740742 

319 

921607 

139 

819135 

458 

180865 

36 

25 

740934 

319 

921524 

139 

819410 

458 

180590 

35 

26 

741125 

319 

921441 

139 

819684 

458 

180316 

34 

27 

741316 

319 

921357 

139 

819959 

458 

180041 

33 

28 

741508 

318 

921274 

139 

820234 

458 

179766 

32 

29 

741699 

318 

921190 

139 

820508 

457 

179492 

31 

30 

741889 

318 

921107 

139 

820783 

457 

179217 

30 

31 

9.742080 

318 

9.921023 

139 

9.821057 

457 

10.17894,3 

29 

32 

742271 

318 

920939 

140 

821332 

457 

178668 

28 

33 

742462 

317 

920856 

140 

821606 

457 

178394 

27 

34 

742652 

317 

920772 

140 

821880 

457 

178120 

26 

35 

742842 

317 

920688 

140 

822154 

457 

177846 

25 

36 

743033 

317 

920604 

140 

822429 

457 

177571 

24 

37 

743223 

317 

920520 

140 

82270S 

457 

177297 

23 

38 

743413 

316 

920436 

140 

822977 

456 

177023 

22 

39 

743602 

316 

920352 

140 

823250 

456 

176750 

21 

40 

743792 

316 

920288 

140 

823524 

456 

176476 

20 

41 

9.743982 

316 

9.920184 

140 

9.823798 

456 

10.176202 

19 

42 

744171 

316 

920099 

140 

824072 

456 

175928 

18 

43 

744361 

315 

920015 

140 

824345 

456 

175655 

17 

44 

744550 

315 

919931 

141 

824619 

456 

175381 

16 

45 

744739 

315 

919846 

141 

824893 

456 

175107 

15 

46 

744928 

315 

919762 

141 

825166 

456 

174834 

14 

47 

745117 

315 

919677 

141 

825439 

455 

174561 

13 

48 

745306 

314 

919593 

141 

825713 

455 

174287 

12 

49 

745494 

314 

919508 

141 

825986 

455 

174014 

11 

50 

745683 

314 

919424 

141 

826259 

455 

173741 

10 

51 

9.745871 

314 

9.919339 

141 

9.826532 

455 

10.173468 

c 

52 

746059 

314 

919254 

141 

826805 

455 

173195 

I 

53 

746248 

313 

919169 

141 

827078 

455 

172922 

1 

54 

746436 

313 

919085 

141 

827351 

455 

172649 

6 

55 

746624 

313 

919000 

141 

827624 

455 

172376 

K 

C 

56 

746812 

313 

918915 

142 

827897 

454 

172103 

4 

57 

746999 

313 

918830 

142 

828170 

454 

171830 

3 

58 

747187 

312 

918745 

142 

828442 

454 

171558 

t 

59 

747374 

312 

918659 

142 

8287  If 

434 

171285 

] 

60 

747562 

312 

918574 

142 

828987 

454 

171013 

0 

J  Oo-siue 

Sine 

Cotang. 

Tang.   |  M. 

56  Dec 


52 


(34  Degrees. )     A  TABLE  or  LOGARITHMIC 


M. 

Sine 

D.   i   Cosine  [  D. 

Tang.   |   D. 

Cotang.  | 

0 

9.747562 

312 

9.918574 

142 

9.828987 

454 

10.171*013 

60 

1 

747749 

312 

918489 

142 

829260 

454 

170740 

59 

2 

747936 

312 

918404 

142 

829532 

454 

170468 

58 

3 

748123 

311 

918318 

142 

829805 

454 

170195 

57 

4 

748310 

311 

918233 

142 

830077 

454 

169923 

56 

5 

748497 

311 

918147 

142 

830349 

453 

169651 

C5 

6 

748683 

311 

918062 

142 

830621 

453 

169379 

54 

7 

748870 

311 

917976 

143 

830893 

453 

169107 

53 

8 

749056 

310 

917891 

143 

831165 

453 

168835 

52 

9 

749243 

310 

917805 

143 

831437 

453 

168563 

51 

10 

749429 

310 

917719 

143 

831709 

453 

168291 

50 

11 

9.749615 

310 

9.917634 

143 

».  831981 

453 

10.168019 

49 

12 

749801 

310 

917548 

143 

832253 

453 

167747 

48 

13 

749987 

309 

917462 

143 

832525 

453 

167475 

47 

14 

750172 

309 

917376 

143 

832796 

453 

167204 

46 

15 

750358 

309 

917290 

143 

833068 

452 

166932 

45 

16 

750543 

309 

917204 

143 

833339 

452 

166661 

44 

17 

750729 

309 

917118 

144 

833611 

452. 

166389 

43 

18 

750914 

308 

917032 

144 

833882 

452 

166118 

42 

19 

751099 

308 

9-16946 

144 

834154 

452. 

165846 

41 

20 

751284 

308 

916859 

144 

834425 

452 

165575 

40 

21 

9.751469 

308 

9.916773 

144 

9.834696 

452 

10,165304 

39 

22 

751654 

308 

916687 

144 

834967 

452 

165033 

38 

23 

751839 

308 

916600 

144 

835238 

452 

164762 

37 

24 

752023 

307 

916514 

144 

835509 

452 

164491 

36 

25 

752208 

307 

916427 

144 

835780 

451 

164220 

35 

26 

752392 

30-7 

916341 

144 

836051 

451 

163949 

34 

27 

752576 

307 

.  916254 

144 

836322 

451 

163678 

33 

28 

752760* 

207 

916167 

145 

836593 

451 

163407 

32' 

29 

752944 

306 

916081 

145 

836864 

451 

163136 

31 

30 

753128 

306 

915994 

145 

837134 

451 

162866 

30 

31 

9.753312 

306 

9.915907 

145 

9.837405 

451 

10.162595 

29 

32 

753495 

306 

915820 

145 

837675 

451 

162325 

28 

33 

753679 

306 

915733 

145 

837946 

451 

162054 

27 

34 

753862 

305 

915646 

145 

838216 

451 

161784 

26 

35 

754046 

305 

915559 

145 

838487 

450 

161513 

25 

36 

754229 

305 

915472 

145 

838757 

450 

161243 

24 

37 

754412 

305 

915385 

145 

839027 

450 

160973 

23 

38 

754595 

305 

915297 

145 

839297 

450- 

160703 

22 

"39 

754778 

304 

915210 

145 

839568- 

450 

160432 

21 

40 

7549GO 

304 

915123 

146 

839838 

450 

160162 

20 

41 

9.755143 

304 

9,9  15035 

146 

9.840108 

450 

HK  159892 

19 

42 

755326 

304 

914948 

146 

840378 

450 

159622 

18 

43 

755508 

304 

914860 

14S 

840647 

450 

159353 

17 

44 

755690 

304 

914773 

146 

840917 

449 

159083 

16 

45 

755872 

303 

914685 

146 

841187 

449 

158813 

15 

46 

756054 

303 

914598 

146 

841457 

449 

158543 

14 

47 

756236   303 

914510 

146 

841726 

449 

158274 

13 

48 

756418 

303 

914422 

146 

841996 

449 

158004 

12 

49 

756600 

303 

914334 

146 

842266 

449 

157734 

11 

50 

756782 

302 

•  914246 

147 

,  842535 

449 

157465 

10 

51 

9.756S63 

302 

9.914158 

147 

9.842805 

449 

10.157195 

9 

52 

757144 

302 

914070 

147 

843074 

449 

156926 

8 

53 

757326 

302 

913982 

147 

843343 

449 

156657 

7 

54 

757507 

302 

913894 

147 

843612 

449 

156388 

6 

55 

757688 

301 

913806 

147 

843882 

448 

156118 

5 

56 

757869 

301 

913718 

147 

844151 

448 

155849 

4 

57 

758050 

301 

913630 

147 

844420 

448 

155580 

3 

58 

758230 

301 

913541 

147 

844689 

448 

155311 

2 

59 

758411 

301 

913453 

147 

844958 

448 

155042 

1 

60 

758591 

301 

913365 

147 

845227 

448 

154773 

0 

Cosine 

1   Sine    I      Colang.             -Tang.   j  M. 

55  Degrees. 


SINES  AND  TATtuE.vrs.     ^36  Degrees.) 


53 


M.  |   Sine   |   D.   |  Cosine   |  D.  |   Tang.     D. 

Cotang. 

0 

9.758591 

301 

9.913365 

147 

9.845227 

448 

10.154773 

60 

1 

758772 

300 

913276 

147 

845496 

448 

154504 

59 

2 

758952 

300 

913187 

148 

845764 

448 

154236 

58 

3 

759132 

300 

913099 

148 

846033 

448 

153967 

57 

4 

759312 

300 

913010 

148 

846302 

448 

153698 

56 

5 

759492 

300 

912922 

148 

846570 

447 

153430 

55 

6 

759672 

299 

912833 

146 

846839 

447 

153161 

54 

7 

759852 

299 

912744 

I4f 

847107 

447 

152893 

53 

8 

760031 

299 

912655 

148 

847376 

447 

152624 

52 

9 

760211 

299 

912566 

148 

847644 

447 

152356 

51 

10 

760390 

299 

912477 

148 

847913 

447 

152087 

50 

11 

9.760569 

298. 

9.912388 

148 

9.848181 

447 

10.151819 

49 

12 

760748 

298 

912299 

1*9 

848449 

447 

151551 

48 

13 

760927 

298 

912210 

149 

848717 

447 

151283 

47 

14 

761106 

298 

912121 

149 

848986 

447 

151014 

46 

15 

761285 

298 

912031 

149 

849254 

447 

150746 

45 

16 

761464 

298 

911942 

149 

849522 

447 

150478 

44 

17 

7616421  297 

911853 

14'J 

849790 

446 

150210 

43 

18 

761821 

297 

911763 

149 

850058 

446 

149942 

42 

19 

761999 

297 

911674 

149 

850325 

446 

149675 

41 

20 

762177 

297 

911584 

149 

850593 

446 

149407 

40 

21 

9.762356 

297 

9.911495 

149 

9.850861 

446 

10.149139 

39 

22 

762534 

296 

911405 

149 

851129 

446 

148871 

38 

23 

762712 

296 

911315 

150 

851396 

446 

148604 

37 

24 

762889 

296 

911226 

150 

851664 

446 

148336 

36 

25 

763067 

296 

911136 

150 

851931 

446 

148069 

35 

26 

763245 

296 

911046 

150 

852  j  99 

446 

147801 

34 

27 

763422 

296 

910956 

150 

852466 

446 

147534 

33 

28 

763600 

295 

910866 

150 

852733 

445 

147267 

32 

29 

763777 

295 

910776 

150 

853001 

445 

146999 

31 

30 

763954 

295 

910686 

150 

853268 

445 

146732 

30 

31 

9.764131 

295 

9.910596 

150  9.853535 

445 

10.146465 

29 

32 

764308 

295 

910506 

150 

853802 

445 

146198 

28 

33 

764485 

294 

910415 

150 

854069 

445 

145931 

27 

34 

764662 

294 

910325 

151 

854336 

445 

145684 

26 

35 

764838   294 

910235 

151 

854603 

445 

145397 

25 

36 

765015 

294 

910144 

151 

854870 

445 

145130 

24 

37 

38 

765193 
765367 

294 
294 

9100541  151 
909963  151 

855137 
855404 

445 

445 

144863 
144596 

23 

22 

39 

765544 

293 

909873!  151 

855671 

444 

144329 

21 

40 

785720 

293 

909782 

151 

855938 

444 

144062 

20 

41 

9  .  765890 

293 

9.909691 

151 

9.856204 

444 

10.143796 

19 

42 

766072 

293 

909601 

151 

856471 

444 

143529 

18 

43 

766247 

293 

909MO 

151 

856737 

444 

143263 

17 

44 

766423 

293 

909419 

151 

857004 

444 

142996 

16 

45 

766598 

292 

909328 

152 

857270 

444 

142730 

15 

46 

766774 

292 

909237 

152 

857537 

444 

142463 

14 

47 

766949 

292 

909146 

152 

857803 

444 

142197 

13 

48 

767124 

292 

909055 

152 

858069 

444 

141931 

12 

49 

767300 

292 

908964 

152 

'  858336 

444 

141664 

11 

50 

767475 

291 

908873 

.152 

858602 

443 

141398 

10 

51 

9.767649 

291 

9.908781 

152 

9.858868 

443 

10.141132 

9 

52 

767824 

291 

908690 

152 

859134 

443 

140866 

8 

53 

767999 

291 

908599 

152 

859400 

443 

140600 

7 

54 

768173 

291 

908507 

152 

859666 

443 

140334 

6 

55 

768348 

290 

908416 

153 

859932 

443 

140068 

5 

56 

768522 

290 

908324 

153 

860198 

443 

139802 

4 

57 

768697 

290 

908233 

153 

860464 

443 

139536 

3 

58 

768871 

290 

908141 

153 

860730 

443 

139270 

2 

59 

769045 

290 

908049 

153 

860995 

443 

139005 

1 

60 

7692191  290 

907958 

153 

861261 

443 

138739 

0 

j   Conine  J       |   Sine         Cotang. 

Tang. 

M. 

5* 


54  Degrees. 


64 


(3G  Degrees.;     A     ABLE  or  LOGARITHMIC 


ML 

Sine   1   D.   1  Cosine   [  D. 

Tang.   (   D.     Cotang. 

0 

9.769219 

290 

9.907958 

153 

9.861261 

443 

10.138739 

60 

1 

769393 

289 

907866 

153 

861527 

443 

138473 

5& 

2 

769566 

289 

907774 

153 

861792 

442 

138208 

58 

3 

769740 

289 

907682 

153 

862058 

442 

137942 

57 

4 

769913 

289 

907590 

153 

862a23 

442 

137677 

56 

5 

770087 

289 

907498 

153 

862589 

442 

137411 

55 

6 

770260 

288 

907406 

153 

862854 

442 

137146 

54 

7 

770433 

288 

907314 

154 

863119 

442 

136881 

53 

8 

770606 

288 

907222 

154 

863385 

442 

136615 

52 

9 

770779 

288 

907129 

154 

863650 

442 

136350 

51 

10 

770952 

288 

907037 

154 

863915 

442 

136085 

50 

11 

9.771125 

288 

9  906945 

154 

9.864180 

•442 

10.135820 

49 

12 

771298 

287 

906852 

154 

864445 

442 

135555 

48 

13 

771470 

287 

906760 

154 

864710 

442 

135290 

47 

14 

771643 

287 

9<M>667 

154 

864975 

441 

135025 

46 

15 

771815 

287 

906575 

154 

865240 

441 

134760 

45 

16 

771987 

287 

906482 

154 

865505 

441 

134495 

44 

17 

772159 

287 

906389 

155- 

865770 

441 

134230 

43 

18 

772331 

286 

906296 

155 

866035 

441 

133965 

42 

19 

772503 

286 

906-204 

155 

866300 

441 

133700 

41 

20 

772675 

286 

906111 

155 

866564 

441 

133436 

40 

21 

9.772847 

286 

9.906018 

155 

9.866829 

441 

10,133171 

39 

22 

773018 

286 

905925 

155 

867094 

441 

132906 

38 

23 

773190 

286 

905832 

155 

867358 

441 

132642 

37 

24 

773361 

285 

305739 

155 

867623 

441 

132377 

36 

25 

773533 

285 

905645 

155 

867887 

441 

132113 

35 

26 

773704 

285 

905>r>52 

155 

8458152 

440 

131848 

34 

27 

773875 

285 

905459 

155 

868416 

440 

131584 

33 

28 

774046 

285 

905366 

156 

868680 

440 

131320 

32 

29 

774217 

285 

905272 

156 

868945 

440 

131055 

31 

30 

774388 

284 

905179 

156 

869209 

440 

130791 

30 

31 

9.774558 

284 

$,905085 

156 

9.869473 

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10.130527 

29 

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284 

904992 

156 

869737 

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13026-3 

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774899 

284 

904898 

156 

870001 

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129999 

27 

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775070- 

284 

904804 

156 

870265 

440 

129735 

26 

35 

775240 

284 

904711 

156- 

870529 

440 

129471 

25 

36 

776410 

283 

904617 

156 

870793 

440 

129207 

24 

37 

775580 

283 

904523 

156 

871057 

440 

128943 

23 

38 

775750 

283 

9044291  157 

871321 

440 

128679 

22 

39 

775920 

283 

904335 

157 

871585 

440 

128415 

21 

40 

776090 

283 

904241 

157 

871849 

439 

128151 

20 

41 

9.776251) 

283 

9.904147 

157 

.9.872112 

439 

10,127888 

19 

42 

776429- 

£S2 

904053 

157 

872376 

439 

127624 

18 

43 

776598 

282 

903959 

157 

872640 

439 

127360 

17 

44 

776768 

282 

903864 

157 

872903 

439 

1  27097 

16 

45 

776937 

28-2 

903770 

157 

873167 

439 

126833 

15 

46 

777  106!  282 

903676 

157 

8-73430 

439 

1265YO 

14 

47 

777275 

281 

903581 

157 

873694 

439 

12G306 

13 

48 

777444 

28-1 

903&87 

157 

873957 

439 

126043 

12 

49 

777613 

281 

903392 

158 

874220 

439 

125780 

11 

50 

777781 

281 

903298 

158 

•  874484 

439 

125516 

10 

51 

9.777950 

281 

9.903203 

158 

9.874747 

439  10,125253 

9 

52 

778119 

281 

903108 

158 

875010 

439 

124990 

8 

53 

778287 

280 

903014 

158 

875273 

438 

124727 

7 

54 

778455 

280 

902919 

158 

875536 

438 

124464 

6 

55 

778624 

280 

902824 

158 

875800 

;  4&8 

124200 

5 

56 

778792 

280 

902729 

158 

876063 

438 

123937 

4 

57 

778960 

280 

902634 

158 

876326 

1  438 

123674 

3 

58 

779128 

280 

902539 

159 

876589 

438 

123411 

2 

59 

779295 

279 

902444 

159 

876851 

:  438 

123149 

1 

60 

779463 

279 

902349'  159 

877114 

;  438 

122886 

0 

Cosine   | 

Sine   1    |   Cotang. 

j    Tang.  |  M. 

Degrees. 


SINES  AND  TANGENTS.     (37  Degrees.) 


55 


M.    Sine   |   D.     Cosine  |  D.  |   Tang.      D.      Cotang.  | 

0 

9.779463 

279 

9.902349 

159 

9.877114 

438 

10.122886 

bO 

1 

779631 

279 

902253 

159 

877377 

438 

122623 

59 

2 

779798 

279 

902158 

159 

877640 

48& 

122360 

58 

3 

779966 

279 

902063 

159 

877903 

438 

122097 

57 

4 

780133 

279 

901967 

159 

878165 

438 

121835 

56 

5 

780300 

278 

901872 

159 

878428 

438 

121572 

55 

6 

780467 

278 

901776 

159 

878691 

438 

121309 

54 

7 

780634 

278 

901681 

159 

878953 

437 

121047 

53 

8 

780801 

278 

901585 

159 

879216 

437 

120784 

52 

9 

780968 

278 

901490 

159 

879478 

437 

120522 

51 

10 

781134 

278 

901394 

160 

879741 

437 

120259 

50 

11 

9.781301 

277 

9.901298 

160 

9.880003 

437 

10.119997 

49 

12 

781468 

277 

£01202 

160 

880265 

437 

119735 

48 

13 

781634 

277 

901106 

160 

880528 

437 

119472 

47 

14 

781800 

277 

901010 

160 

880790 

437 

119210 

46 

15 

781966 

277 

900914 

160 

881052 

437 

118948 

45 

16 

782132 

277 

900818 

161 

881314 

437 

118686 

44 

17 

782298 

276 

900722 

160 

881576 

437 

118424 

43 

18 

782464 

276 

900626 

160 

881839 

437 

118161 

42 

19 

782630 

276 

900529 

160 

882101 

437 

117899 

41 

20 

782796 

276 

900433 

161 

882363 

436 

117637 

40 

21 

9.782961 

276 

9.900337 

161 

9.882625 

436 

10.117375 

39 

22 

783127 

276 

900240 

•161 

882887 

436 

117113 

38 

23 

733292 

275 

900144 

161 

883148 

436 

116852 

37 

24 

783458 

275 

900047 

161 

883410 

436 

116590 

36 

25 

783623 

275 

899951 

161 

883672 

436 

116328 

35 

26 

783738 

275 

899354 

161 

883934 

436 

116066 

34 

27 

783953 

275 

899757 

161 

834196 

436 

115804 

33 

28 

784118 

275 

899660 

161 

884457 

436 

115543 

32 

29 

784282 

274 

899564 

161 

884719 

436 

115281 

31 

30 

784447 

274 

899467 

162 

884980 

436 

115020 

30 

31 

9.784612 

274 

9.899370 

162 

9  .  885242 

436 

10.114758 

29 

32 

784776 

274 

899273 

162 

885503 

436 

114497 

28 

33 

784941 

274 

899176 

162 

885765 

436 

1  14235 

27 

34 

785105 

274 

899078 

162 

8S6026 

436 

113974 

26 

35 

785269 

273 

893931 

162 

886238 

436 

113712 

25 

36 

785433 

273 

893834 

162 

886549 

435 

113451 

24 

37 

785597 

273 

898787 

162 

880810 

435 

113190 

23 

38 

78576  1 

273 

893689 

162 

887072 

435 

112928 

22 

39 

735925 

273 

893592 

162 

887333 

435 

112667 

21 

40 

786089 

273 

898494 

163 

887594 

435 

112406 

20 

41 

9.736252 

272 

9.893397 

163 

9.887855 

435 

10.112145 

19 

42 

786416 

272 

8982J9 

163 

888116 

435 

111884 

13 

43 

786579 

272 

893202 

163 

883377 

435 

111623 

17 

44 

786742 

272 

893104 

I63i   833639 

435 

111361 

16 

45 

786906 

272 

893006 

163 

838900 

435 

111100 

15 

46 

787069 

272 

897908 

163 

839160 

435 

1  10840 

14 

47 

787232 

271 

897810 

163 

889421 

435 

110579 

13 

48 

787395 

271 

897712 

163 

889682 

435 

110318 

12 

49 

787557 

271 

897614 

163 

889943 

435 

110057 

11 

50 

787720 

271 

897516 

163 

890204 

434 

109796 

10 

51 

9.787883 

271 

9.897418 

164 

9.890465 

434 

10.109535 

9 

52 

788045 

271 

897320 

164 

890725 

434 

109275 

8 

53 

788208 

271 

897222 

164 

890986 

434 

109014 

7 

54 

783370 

270 

897123 

164 

891247 

434 

108753 

6 

55 

788532 

270 

897025 

164 

891507 

434 

108493 

X 
tJ 

56 

788694 

270 

896926 

164 

891768 

434 

108232 

4 

57 

788856 

270 

89682S 

164 

892028 

434 

107972 

q 

58 

789018 

270 

896729 

164 

892289 

434 

107711 

2 

59 

789180 

270 

896631 

164 

892549 

434 

107451 

1 

60 

789342 

269 

896532 

164 

892810 

434 

107190 

0 

Cosine 

Sine 

Cotang. 

Tang.   j 

52  Degrees 


56 


(38  Degrees.)     A  TABLE  OF  LOGARITHMIC 


M.  |   Sine      I).   |   r,«,iiM.   |  D.    Tan*   |   D. 

Cotang.  | 

0 

9.789342 

269 

9.890532 

164 

9.892810 

434 

10.107190-60 

1 

789504 

269 

896433 

165 

893070 

434 

106930 

59 

2 

•  789665 

269 

896335 

165 

893331 

434 

106669 

58 

3 

789827 

269 

896236 

165 

893591 

434 

106409 

57 

4 

789988 

269 

896137 

165 

893851 

434 

106119 

56 

5 

790149 

269 

896038 

165 

894111 

434 

105889 

55 

6 

790310 

268 

895939 

165 

894371 

434 

105629 

54 

7 

790471 

268 

895840 

165 

894632 

433 

105368 

53 

8 

790632 

268 

895741 

165 

894892 

433 

105108 

52 

9 

790793 

268 

895641 

165 

895152 

433 

104848 

51 

10 

790954 

268 

895542 

165 

895412 

433 

104588  50 

11 

9.791115 

268 

9.895443 

166 

9.895672 

433 

10,104328  49 

12 

791275 

267 

895343 

166 

895932 

433 

104068 

48 

13 

791436 

267 

895244 

166 

896192 

433 

103808 

47 

14 

791596 

267 

895145 

166 

896452 

433 

103548 

46 

15 

791757 

267 

895045 

166 

896712 

433 

103288 

45 

16 

791917 

267 

894945 

166 

896971 

433 

103029 

44 

17 

792077 

267 

894846 

166 

897231 

433 

102769 

43 

18 

792237 

266 

894746 

166 

897491 

433 

102509 

42 

19 

792397 

266 

894646 

166 

897751 

433 

102249 

41 

20 

792557 

266 

894546 

166 

898010 

433 

101990 

40 

21 

9.792716 

266 

9.894446 

167 

9.898270 

433 

10.101730 

39 

22 

792876 

266 

894346 

167 

898530 

433 

101470 

38 

23 

793035 

266 

894246 

167 

898789 

433 

101211 

37 

24 

793195 

265 

894146 

167 

899049 

432 

100951 

36 

25 

793354 

265 

894046 

167 

899308 

432 

100692 

35 

26 

793514 

265 

893946 

167 

899568 

433 

100432 

34 

27 

793673 

265 

893846 

167 

899827 

432 

100173 

33 

28 

793832 

2G5 

893745 

187 

900086 

432 

099914 

32 

29 

793991 

265 

893645 

167 

900346 

432 

099654 

31 

30 

794150 

264 

.  893544 

167 

900605 

432 

099395 

30 

31 

9.794308 

264 

9.893444 

168 

9.900864 

432 

10.099136 

29 

32 

794467 

264 

893343 

168 

901124 

432 

09887-6 

28 

33 

794626 

264 

893243 

168 

901383 

432 

098617 

27 

34 

794784 

264 

893142 

168 

901642 

432 

098358 

26 

35 

794942 

264 

893041 

168 

901901 

432 

098099 

25 

36 

795101 

264 

89294-0 

168 

902160 

432 

097840 

24 

37 

795259 

263 

892839 

168 

902419 

432 

097581 

23 

38 

795417 

263 

892739 

168 

902679 

432 

097321 

22 

39 

795575 

203 

892638 

168 

902938 

432 

097062 

21 

40 

795733 

263 

•  892536 

168 

903197 

431 

096803 

20 

41 

9.795891 

263 

9.892435!  169 

9.903455 

431 

10.096545 

19 

42 

796049 

263 

892334 

169 

903714 

431 

096286 

18 

43 

796206 

263 

892233 

169 

903973 

431 

096027 

17 

44 

796364 

262 

892132 

169 

904232 

431 

095768 

16 

45 

796521 

262 

892030 

169 

904491 

431 

095509 

15 

46 

796679 

262 

891929 

169 

904750 

431 

095250 

14 

47 

796836 

262 

891827 

169 

905008 

431 

094992 

13 

48 

796993 

262 

891726 

169 

905267 

431 

094733 

12 

49 

797150 

261 

891624 

169 

905526 

431 

094474 

11 

50 

797307 

261 

891523 

170 

905784 

431 

094216 

10 

51 

9.797464 

261 

9.891421 

170 

9  .  906043 

431 

10.093957 

9 

52 

797621 

261 

891319 

170 

906302 

431 

093698 

8 

53 

797777 

261 

891217 

170 

90S560 

431 

093440 

7 

54 

797934 

261 

891115 

170 

906819 

431 

093181 

6 

55 

79S091 

261 

891013 

170 

907077 

431 

092923 

5 

56 

79S247 

261 

890911 

170 

907336 

431 

092664 

4 

57 

798403 

260 

890809 

170 

907594 

431 

092406 

3 

58 

798560 

260 

890707 

170 

907852 

431 

092148 

2 

59 

798716 

260 

890605 

170 

908111 

430 

091889 

1 

60 

798872 

260 

890503 

170 

'  908369 

430 

091631 

0 

{  Cosine   J      |   Sine 

|  Cotang.  | 

Tang.   1  M. 

31  Decrees. 


SINES  AND  TANGENTS.      (39  Degrees.) 


M. 

Sine 

D. 

Cosine    D.    Tang.  |   D.   |   Cotang. 

0 

9.798872 

260 

9.890503 

170 

9.908369 

430 

10.091631 

60 

1 

799028 

260 

890400 

171 

908628 

430 

091372 

59 

2 

799184 

260 

890298 

171 

908886 

430 

091114 

58 

3 

799339 

259 

890195 

171 

909144 

430 

090856 

57 

4 

799495 

259 

890093 

171 

909402J  430 

090598 

66 

5 

799651 

259 

889990 

171 

909660   430 

090340 

55 

6 

799806 

259 

889888 

171 

909918   430 

090082 

54 

7 

799962 

259 

889785 

171 

910177   430 

089823  53 

8 

800117 

259 

889682 

171 

910435J  430 

089565  52 

9 

800272 

258 

889579 

171 

910693   430 

08930?  51 

10 

800427 

258 

889477 

171 

910951!   430 

089049 

50 

11 

9.800582 

258 

9.889374 

172 

9.911209;   430 

10.088791 

49 

12 

800737 

258 

889271 

172 

911467J   430 

088533 

48 

13 

800892 

258 

889168 

172 

911724!   430 

088276 

4? 

14 

801047 

258 

889064 

172 

911982!   430 

088018 

40 

15 

801201 

258 

888961 

172 

912240:  430 

087760 

45 

16 

801356 

257 

888858 

172 

912498!  430 

087502 

44 

17 

801511 

257 

888755 

172 

912756 

430 

087244 

43 

18 

801665 

257 

888651 

172 

913014 

429 

0869S6 

42 

19 

801819 

257 

888548 

172 

913271 

429 

086729 

41 

20 

801973 

257 

888444 

173 

913529 

429 

086471 

40 

21 

9.802128 

257  9.888341 

173 

9.913787 

429 

10.086^13 

39 

22 

802282 

256 

888237 

173 

914044 

429 

085956 

38 

23 

802436 

256 

888134 

173 

914302 

429 

085698 

37 

24 

802589 

256 

888030 

173 

914560 

429 

085440 

36 

25 

802743 

256 

887926 

173 

914817 

429 

085183 

35 

26 

802897 

256 

887822 

173 

915075 

429 

084925 

34 

27 

803050 

256 

887718 

173 

915332 

429 

084668 

33 

28 

803204 

256 

887614 

173 

915590 

429 

084410 

32 

29 

803357 

255 

887510 

173 

915847 

429 

084153 

31 

30 

803511 

255 

887406 

174 

916104 

429 

083896 

30 

31 

9.803664 

255 

9.887302 

174 

9.916362 

429 

10.083638 

29 

32 

803817 

255 

887198 

174 

916619 

429 

083381 

28 

33 

803970 

255 

887093 

174 

916877 

429 

•  083123 

2? 

34 

804123 

255 

886989 

174 

917134 

429 

082866 

26 

35 

804276 

254 

886885 

174 

917391 

429 

OS2609 

25 

36 

804428 

254 

886780 

174 

917648 

429 

082352 

24 

3!T 

804581 

254 

886676 

174 

917905 

429 

082095 

23 

38 

804734 

254 

886571 

174 

918163!  428 

08183? 

22 

39 

804886 

254 

8S6466 

174 

918420;  428 

OS1  580 

21 

40 

805039 

254 

886362 

175 

918677 

428 

081323 

20 

41 

9.805191 

254 

9.886257 

175 

9.918934 

428 

10.081066 

19 

42 

805343 

253 

886152 

175 

919191 

428 

080809 

18 

43 

805495 

253 

886047 

175 

919448 

428 

080552 

17 

44 

805647 

253 

885942 

175 

919705 

428 

080295 

16 

45 

805799 

253 

885837 

175 

919962 

428 

080038 

15 

46 

805951 

253 

885732 

175 

920219   428 

079781 

14 

47 

806103 

253 

885627 

175 

9204761  428 

079524 

13 

48 

806254 

253 

885522 

175 

920733 

428 

079267 

12 

49 

806406 

252 

885416 

175 

920990 

428 

079010 

11 

50 

806557 

252 

885311 

176 

921247 

428 

078753 

10 

51 

9.806709 

252  9.885205 

176 

9.921503!  428 

10.078497 

9 

52 

806860 

252 

885100 

176 

921760 

428 

078240 

8 

53 

807011 

252 

884994 

176 

922017 

428 

077983 

7 

54 

807163 

252 

884889 

176 

922274J  428 

077726 

6 

55 

807314 

252 

884783 

176 

922530   428 

077470 

5 

56 

807465 

251 

884677 

176 

922787   428 

077213 

4 

57 

807615 

251 

884572 

176 

9230441  428 

076956 

3 

58 

807766 

251 

884466 

176 

923300 

428 

076700 

2 

59 

807917 

251 

884360 

176 

923557 

427 

076443 

1 

60 

8080671  251 

884254 

17? 

923813 

427 

076187 

0 

Cosine 

Sine 

1   Cotang.  1 

Tang.    |  M. 

50  Degrees. 


58 


(40  Degrees.^     A  TABLE  OF  LOGARITHMIC 


M.     S-ne      D.    Cosine   |  D.     Tang.     I).      Cotanp. 

0 

9.808067 

251 

9.884254!  177 

9.923813   427 

10.076187 

60 

1 

808218 

251 

884148 

177 

924070 

427 

075930 

59 

<J 

808368 

251 

884042 

177 

924327 

427 

075673 

58 

3 

808519 

250 

883936 

177 

924583 

427 

075417 

57 

4 

808669 

250 

883829 

177 

924840 

427 

075160 

56 

5 

808819 

250 

883723 

177 

925096 

427 

074904 

55 

6 

808969 

250 

883617 

177 

925352 

427 

074648 

54 

7 

809119 

250 

883510 

177 

925609 

427 

074391 

53 

8 

809269 

250 

883404 

177 

925S65 

427 

074135 

52 

9 

809419   249 

883297 

178 

926122 

427 

073878 

51 

10 

8095691   249 

883191 

178 

926378 

427 

073622 

50 

11 

9.809718   249 

9.883084 

178 

9.926634 

427 

10.073366 

49 

12 

809868 

249 

882977 

178 

92««90 

427 

073110 

48 

13 

810017 

249 

882871 

178 

927147 

427 

072853 

47 

14 

.  810167 

249 

882764 

178 

927403 

427 

072597 

46 

15 

810316 

248 

882657 

178 

927659 

427 

072341 

45 

16 

810465 

248 

882550 

178 

927915 

427 

072085 

44 

17 

810614 

248 

882443 

178 

928171 

427 

071829 

43 

18 

810763 

248 

882336 

179 

928427 

427 

071573 

42. 

19 

810912 

248 

882229 

179 

928683 

427 

071317 

41 

20 

8i:06l|  248 

882121 

179 

928940 

427 

071060 

40 

21 

9.8112101  248 

9.882014 

179 

9.929196 

427 

10.070804 

39 

22 

811358!  747 

881907 

179 

929452 

427 

070548 

38 

23 

811507 

247 

881799 

179 

929708 

427 

070292 

37 

24 

811655 

247 

881692 

179 

929964 

426 

070036 

36 

25 

811804 

247 

881584 

179 

930220 

426 

069780 

35 

26 

811952   247 

881477 

179 

930475 

426 

069525 

34 

27 

812100J  247 

881369 

179 

930731 

426 

069269 

33 

28 

812248   247 

881261 

180 

930987 

426 

069013 

32 

29 

812396!  246 

881153 

180 

931243 

426 

068757 

31 

30 

812544!  246 

881046 

180 

931499 

426 

068501 

30 

31 

9.812692 

246 

9.880938 

180 

9.931755 

426 

10.068245 

29 

32 

812840   246 

880830 

180 

932010 

426 

067990 

28 

33 

8129881  246 

880722 

180 

932266 

426 

067734 

27 

34 

813135   246 

880613 

180 

932522 

426 

067478 

26 

35 

8132831  246 

880505 

180 

932778 

426 

067222 

25 

36 

813430!   245 

880397 

180 

933033 

426 

066967 

24 

37 

813578   245 

880289 

181 

933289 

426 

066711 

23 

38 

813725!   245 

880180 

181 

933545 

426 

066455 

22 

39 

813872   245 

880072 

181 

933800 

426 

066200 

21 

40 

8l40l9i  245 

879963 

181 

934056 

426 

065944 

20 

41 

9.814166   245 

9.879855 

181 

9.9J4311 

426 

10.065689 

19 

42 

814313   245 

879746 

i81 

934567 

426 

065433 

18 

43 

814460 

244 

879637 

181 

934823 

426 

065177 

17 

44 

814607)  244 

879529 

181 

935078 

426 

064922 

16 

45 

814753   244 

879420 

181 

935333 

426 

064667 

15 

46 

81  4900  1  244 

879311 

181 

935589 

426 

064411 

14 

47 

815046   244 

879202 

182 

036844 

426 

064156 

13 

48 

815193   244 

879093 

182 

938100 

426 

063900 

12 

49 

815339   244 

878984 

182 

936355 

426 

063645 

11 

50 

815485   243 

878875 

182 

936610 

426 

063390 

10 

51 

9.815631   243 

9.878766 

182 

9.936866 

425 

10.063134 

9 

52 

815778   243 

878656 

182 

937121 

425 

062S79 

8 

53 

815924   243 

878547  182 

937376 

425 

062624 

7 

54 

816069   243 

878438  182 

937632 

425 

062368 

6 

55 

816215   243 

878328  182 

937887 

425 

062113 

5 

56 

816361 

243 

878219!  183 

938142 

425 

061858 

4 

57 

816507 

242 

878109  183 

938398 

425 

061602 

3 

58    816652 

242 

877999;  183 

938653 

425 

061347 

2 

59 

816798 

242 

877890!  183 

938908 

425 

061  092 

1 

60 

8169431  242    877780  183 

939163 

425 

060837 

0 

1  Cosine 

Sine    1    I  Colang.   1 

Tang.' 

M. 

48  Degre 


SINES  AND 


Degrees.} 


M. 

Sine 

D. 

Cosine  |  D.  |   Tarifr. 

D.   j    Cotang. 

0 

9.816943 

242 

9.877780 

183 

9.939163 

425 

10.060837 

60 

1 

817088 

242 

877670 

183 

939418 

425 

060582 

59 

2 

817233 

242 

877560 

183 

939673 

425 

060327 

58 

3 

817379 

242 

877450 

183 

939928 

425 

060072 

57 

4 

817524 

24] 

877340 

183 

940183 

425 

059817 

56 

5 

817668 

241 

877230 

184 

940438 

425 

059562 

55 

6 

817813 

241 

877120 

184 

940694 

425 

059306 

54 

7 

817958 

241 

877010 

184 

940949 

425 

059051 

53 

8 

818103 

241 

876899 

184 

941204 

425 

058796 

52 

9 

818247 

241 

876789 

184 

941458 

425 

058542 

51 

10 

818392 

241 

876678 

184 

941714 

425 

058286 

50 

11 

9.818536 

240 

9.876568 

184 

9.941968 

425 

10.058032 

49 

12 

818681 

240 

876457 

184 

942223 

425 

057777 

48 

13 

818825 

240 

876347 

1.84 

942478 

425 

057522 

47 

14 

818969 

240 

-876236 

185 

942733 

425 

057267 

46 

15 

819113 

240 

876125 

185 

942988 

425 

057012 

45 

Ifi 

819257 

240 

876014 

185 

943243 

425 

056757 

44 

17 

819401 

240 

875904 

185 

943498 

425 

056502 

43 

18 

819545 

239 

875793 

185 

943752 

425 

056248 

42 

19 

819689 

239 

875682 

185 

944007 

425 

055993 

41 

20 

819832 

239 

875571 

185 

944262 

425 

055738 

40 

21 

0.819976 

239 

9.875459 

185 

9.944517 

425 

10.0554831  39 

22 

820120 

239 

875348 

185 

944771 

424 

055229  38 

23 

820263 

239 

875237 

185 

945026 

424 

054974  1  37 

24 

820406 

239 

875126 

186 

945281 

424 

054719 

36 

25 

820550 

238 

875014 

186 

945535 

424 

054465 

35 

26 

820693 

238 

'  874903 

186 

945790 

424 

054210 

34 

27 

820836 

238 

874791 

186 

946045 

424 

053955 

33 

28 

820979 

238 

874680 

186 

946299 

424 

053701 

32 

29 

821122 

238 

874568 

186 

946554 

424 

053446 

31 

30 

821265 

238 

874456 

186 

946808 

424 

053192  30 

31 

9.821407 

238 

9.874344 

186 

9.947063 

424 

10.0529371  29 

32 

821550 

238 

874232 

187 

947318 

424 

052682  28 

33 

821693 

237 

874121 

187 

947572 

424 

052428 

27 

34 

821835 

237 

874009 

187 

947826 

424 

052  1  74 

26 

35 

821977 

237 

873896 

187 

948081 

424 

051919 

25 

36 

822120 

237 

8737S4 

187 

948336 

424 

051664 

24 

37 

822262 

237 

873672 

187 

9485% 

•424 

051410 

23 

38 

822404 

237 

873560 

187 

948844 

424 

051156 

22 

39 

822546 

237 

873448 

187 

949099 

424 

050901 

21 

40 

822688 

236 

873335 

187 

949353   424 

050647 

20 

41 

9.822830   236 

9.873223 

187 

9  .  949607 

424 

10.050393 

19 

42 

822972 

230 

873110 

188 

949862 

424 

050138 

18 

43 

823114 

236 

872998 

188 

950116 

424 

049884 

17 

44 

823255 

236 

872885 

188 

950370 

424 

049630 

16 

45 

823397 

236 

872772  1  388 

950625 

424 

049375 

15 

46 

823539 

236 

872659 

188 

950879 

424 

049  1  2  1 

14 

47 

823680 

235 

872547 

188 

951133 

424 

048867 

13 

48 

823821 

235 

872434 

188 

951388 

424 

04S612 

12 

49 

823963 

235 

87232  J 

188 

951642 

424 

048358 

11 

50 

824104 

235 

872208 

188 

951896 

424 

048104 

10 

51 

52 

9.8242451  235 

824386   235 

9.872095 
871981 

189 
189 

9.952150 
952405 

424 
424 

10.047850 
047595 

9 

8 

53 

824527 

235 

871868 

189 

952659 

424 

047341 

7 

54 

824668 

234 

871755 

189 

952913 

424 

047087 

6 

55 

824808 

234 

871641 

189 

953167 

423 

046833 

5 

56 

824949   234 

871528 

189 

953421 

423 

046579 

4 

57 

825090]  234 

871414 

189 

953675 

423 

046325 

3 

58 

825230 

234 

871301 

189 

953929 

423 

046071 

2 

59 

825371 

234 

871187 

189 

954183 

423 

045817 

1 

60 

825511 

234 

87  i  073 

190 

954437 

423 

045563 

0 

Cosine 

Sine       1  Totang   1      j    Tsxig. 

M. 

Drgrees. 


60 


(42  Degrees.)     A  TABLE  or  LOGARITHMIC 


.  M.  |   Sine 

D.     Cosine   |  D.    Tang.     D.     Cotang. 

0 

9.825511 

234 

9.871073 

190 

9.954437   423 

10.045563 

60 

1 

825651 

233 

870960 

190 

954691!  423 

045309 

59 

2 

825791 

233 

870846 

J90 

954945 

423 

045055 

58 

3 

825931 

233 

870732 

190 

955200 

423 

044800 

57 

4 

826071 

233 

870618 

190 

955454 

423 

044546 

56 

5 

826211 

233 

870504 

190 

955707 

423 

044293 

55 

6 

826351 

233 

870390 

190 

955961 

423 

044039 

54 

7 

826491 

233 

870276 

190 

956215 

423 

043785 

53 

8 

826631 

233 

870161 

190 

956469 

423 

043531 

52 

9 

826770 

232 

87004? 

191 

956723 

423 

043277 

51 

10 

826910 

232 

869933 

191 

956977 

423 

043023 

50 

11 

9.827049 

232 

9.869818 

191 

9.957231 

423 

10.042769 

49 

12 

827189 

232 

869704 

191 

957485 

423 

042515 

48 

13 

827328 

232 

869589 

191 

957739 

423 

042261 

47 

14 

827467 

232 

869474 

191 

957993 

423 

042007 

46 

16 

827606 

232 

869360 

191 

958246 

423 

041754 

45 

16 

827745 

232 

869245 

191 

958500 

423 

041500 

44 

17 

827884 

231 

869130 

191 

958754 

423 

041246 

43 

18 

828023 

231 

869015 

192 

959008 

423 

040992 

42 

19 

828162 

231 

868900 

192 

959262 

423 

040738 

41 

20 

828301 

231 

868785 

192 

959516 

423 

040484 

40 

21 

9.828439 

231 

9.868670 

192 

9.959769 

423 

10.040231 

39 

22 
23 

828578 
828716 

231 
231 

868555 
868440 

192 
192 

960023 
960277 

423 
423 

0399771  38 
039723  37 

24 

828855 

230 

868324 

192 

9G0531 

423 

039469 

36 

25 

828993 

230 

868209 

192 

960784 

423 

039216 

35 

26 

829131 

230 

868093 

192 

961038 

.  423 

038962 

34 

27 

829269 

230 

867978 

193 

961291 

423 

038709 

33 

28 

829407 

230 

867862 

193 

961545 

423 

038455 

32 

29 

829545 

230 

867747 

193 

961799 

423 

038201 

31 

30 

829683 

230 

867631 

193 

962052 

423 

037948 

30 

31 

9.829821 

229 

9.867515 

193 

9  .  962306 

423 

10.037694 

29 

32 

829959 

229 

867399 

193 

962560 

423 

037440 

28 

33 

830097 

229 

867283 

193 

962813 

423 

037187 

27 

34 

830234 

229 

867167 

193 

963067 

423 

036933 

26 

35 

830372 

229 

867051 

193 

9G3320 

423 

036680 

25 

36 

830509   229 

866935 

194 

963574 

423 

036426 

24 

37 

830646 

229 

866819 

194 

963827 

423 

036173 

23 

38 

830784 

229 

866703 

194 

9(54081 

423 

035919 

22 

39 

830921 

228 

866586!  194 

964335 

423 

035665 

21 

40 

831058 

228 

866470 

194 

954588 

422 

035412 

20 

41 

9.831135 

228 

9.866353 

194 

9.964842 

422 

10.035158 

19 

42 

831332 

228 

866237 

194 

965095 

422 

034905 

18 

43 

831469 

228 

866120 

194 

965349 

422 

034651 

17 

44 

831606 

228 

866004 

195 

965602 

422 

034398 

16 

45 

831742 

228 

8G58S7 

195 

965855 

422 

034145 

15 

46 

831879 

228 

805770 

195 

966109 

422 

033891 

14 

47 

832015 

227 

865653 

195 

966362 

422 

033638 

13 

46 

832152 

227 

865536 

195 

966616 

422 

033384 

12 

49 

832288 

227 

865419 

195 

966869 

422 

033131 

11 

50 

832425 

227 

865302  |  195 

967123 

422 

032877 

10 

51 

9.832561 

227 

9.8651851  195 

9.967376 

422 

10.032624 

9 

52 

832697 

227 

865068 

195 

967629 

422 

032371 

8 

53 

832833 

227 

864950 

195 

967883 

422 

032117 

7 

54 

832969 

226 

864833 

196 

968136 

422 

031864 

6 

55 

833105 

226 

864716 

196 

968389 

422 

031611 

5 

56 

833241 

226 

864598  196 

968643 

422 

031357 

4 

57 

833377 

226 

864481 

196 

968896 

422 

031104 

3 

58 

833512 

226 

864363 

196 

969149 

422 

030851 

2 

59 

833648 

226 

864245 

196 

969403 

422 

030597 

1 

60 

833783 

220 

864127 

196 

069656 

422 

030344 

0 

j   Cw  hie  1 

Sim-         |  C  ',:,:,„,.   | 

Taug.    M. 

SINES  AND  TANGENTS.      (43  Degrees.) 


61 


M.  |   Sine   |   D.     Cosine    D.  |   TanC.      D.      Cotang.  | 

0 

9.833783 

226 

9.864127 

196 

9.969656 

422 

10.030344)60 

1 

833919 

225 

864010 

196 

969909 

422 

030091  59 

2 

834054 

225 

883892 

197 

970162 

422 

029838!  58 

3 

834189 

225 

863774 

197 

970416 

422 

029584 

57 

4 

834325 

225 

863656 

197 

970669 

422 

029331 

56 

5 

834460 

225 

863538 

197 

970922 

422 

029078 

55 

6 

834595 

225 

863419 

197 

971175 

422 

028825 

54 

7 

834730 

225 

863301 

197 

971429 

422 

028571 

53 

8 

834S65 

225 

863183 

197 

971682 

422 

028318 

52 

9 

834999 

224 

863064 

197 

971935 

422 

028065 

51 

10 

835134 

224 

862946 

198 

972188 

422 

027812 

50 

11 

9.835269 

224 

9.862827 

198 

9.972441 

422 

10.027559 

49 

12 

835403 

224 

862709 

198 

972694 

422 

027306 

48 

13 

835538 

224 

862590 

198 

972948 

422 

027052 

47 

14 

835672 

224 

86247  i 

19H 

973201 

422 

026799 

46 

15 

835807 

224 

862353 

198 

973454 

422 

026546 

45 

16 

835941 

224 

862234 

198 

973707 

422 

026293 

44 

17 

836075 

223 

862115 

198 

973960 

422 

026040 

43 

18 

836209 

223 

861996 

198 

974213 

422 

025787 

42 

19 

836343 

223 

861877 

198 

974466 

422 

025534 

41 

20 

836477 

223 

861758 

199 

974719 

422 

025281 

40 

21 

9.836611 

223 

9.861638 

199 

9.974973 

422 

10.025027 

39 

22 

836745 

223 

861519 

199 

975226 

422 

024774 

38 

23 

836878 

223 

861400 

199 

975479 

422 

024521 

37 

24 

8370  1  2 

222 

«61280 

199 

975732 

422 

024268 

36 

25 

837  i46 

222 

861161 

199 

975985 

422 

024015 

35 

26 

837279 

222 

861041 

199 

976238 

422 

023762 

34 

27 

837412 

222 

860922 

199 

976491 

422 

023509 

33 

28 

837546 

222 

860802 

199 

976744 

422 

023256 

32 

29 

837679 

222 

860682 

200 

976997 

422 

023003 

31 

30 

837812' 

222 

860562 

200 

977250 

422 

022750 

30 

31 

9.837945 

222 

9.860442 

200 

9.977503 

422 

10.022497 

29 

32 

838078 

221 

860322 

200 

977756 

422 

022244 

28 

33 

838211 

221 

860202 

200 

978009 

422 

021991 

27 

34 

838344 

221 

860082 

200 

978262 

422 

021738 

26 

35 

838477 

221 

859962 

200 

978515 

422 

021485 

25 

36 

838610 

221 

859842 

200 

978768 

422 

021232 

24 

37 

838742 

221 

859721 

201 

97902  1 

422 

020979 

23 

3ft 

838875 

221 

859601 

201 

979274 

422 

020726 

22 

39 

839007 

221 

859480 

201 

979527 

422 

020473 

21 

40 

839140 

220 

859360 

201 

979780 

422 

020220 

20 

41 

9.839272 

220 

9.859239 

201 

9.980033 

422 

10.019967 

19 

42 

839404 

220 

859119 

201 

980286 

422 

019714 

18 

43 

839536 

220 

85S998 

201 

980538 

422 

019462 

17 

44 

839668 

220 

858877 

201 

980791 

421 

019209 

16 

45 

839800 

220 

858756 

202 

981044 

421 

018956 

15 

46 

839932 

920 

858635 

202 

981297 

421 

018703 

14 

47 

840064 

219 

858514 

202 

981550 

421 

018450 

13 

48 

840196 

219 

858393 

202 

981803 

421 

018197 

12 

49 

840328 

219 

858272 

202 

982056 

421 

017944 

11 

50 

840459 

219 

858151 

202 

982309 

421 

017691 

10 

51 

9.840591 

219 

9.858029 

202 

9.982562 

421 

10.017438 

9 

52 

840722 

219 

857908 

202 

982814 

421 

017186 

8 

53 

840854 

219 

857786 

202 

983067 

421 

016933 

7 

54 

840985 

219 

857665 

203 

983320 

421 

016680 

6 

55 

841116 

218 

857543 

203 

983573 

421 

016427 

5 

56 

841247 

218 

857422 

203 

983826 

421 

016174 

4 

57 

841378 

218 

857300 

203 

984079 

421 

015921 

3 

58 

84  1  509 

.  218 

857178 

203 

9^4331 

421 

015669 

2 

59 

841640 

218 

857056 

203 

984584 

421 

015416 

1 

60 

841771 

218 

856934 

?f)3 

984837 

421 

015163  0 

Cwiitfl 

Sine   1 

Cntanjr   j 

Tang. 

M. 

46  Degrees. 


62 


(44  Degrees.)     A  TABLE  OF  LOGARITHMIC 


M.    Sine   |   D.  .  j   Cosine  j  D.  |   Tang.     D.   |   Cotang.   | 

0 

9.841771 

218 

9  .  856934 

203 

9.984837 

421 

10.015163 

60 

1 

841902 

218 

856812 

203 

985090 

421 

014910 

59 

2 

842033 

218 

856690 

204 

985343 

421 

014657 

58 

3 

842163 

217 

856568 

204 

985696 

421 

014404 

57 

4 

842294 

217 

856446 

204 

985848 

421 

014152 

56 

5 

842424 

217 

856323 

204 

986101 

421 

013899 

55 

6 

842555 

217 

858201 

204 

986354 

421 

013646 

54 

7 

842685 

217 

856078 

204 

986607 

421 

013393 

53 

8 

842815 

217 

855956 

204 

986360 

421 

013140 

52 

9 

842946 

217  1   855833 

204 

987112 

421     012888 

51 

10 

843076 

217  |   855711 

205 

987365 

421 

012635 

50 

11 

9.843206 

216 

9.855588 

205 

9.987618 

421 

10.012382 

49 

12 

843336 

216 

855465 

205 

987871 

421 

012129 

48 

13 

8.43466 

216 

855342 

205 

988123 

421 

011877 

47 

14 

843595 

216 

855219 

205 

988376 

421 

011624 

46 

15 

843725 

216 

855096 

205 

988629 

421 

011371 

45 

16 

843855 

216 

854973 

205 

988882 

421 

011118 

44 

17 

843984 

216 

854850 

205 

989134 

421 

010866 

43 

18 

844114 

215 

854727 

206 

989387 

421 

010613 

42 

19 

844243 

215 

854603 

206 

989640 

421 

010360 

41 

20 

844372 

215 

854-180 

206 

989893 

421 

010107 

40 

21 

9.844502 

215 

9.854356 

206 

9.990145 

421 

10.009855 

39 

22 

844631 

215 

854233 

206 

990398 

421 

009602 

38 

23 

844760 

215 

854109 

206 

990651 

421 

009349 

37 

24 

844889 

215 

853986 

206 

990903 

421 

009097 

36 

25 

845018 

215 

853862 

206 

991156 

421 

008844 

35 

26 

845147 

215 

853738 

206 

991409 

421 

008591 

34 

27 

845276 

214 

853614 

207 

991662 

421 

008338 

33 

28 

845405 

214 

853490 

207 

991914 

421 

008086 

32 

29 

845533 

214 

853366 

207 

992167 

421 

007833 

31 

30 

845662 

214 

853242 

207 

992420 

421 

0075SO 

30 

31 

9.845790 

214 

9.853118 

207 

9.992672 

421 

10.007338 

29 

32 

845919 

214 

852994 

207 

992925 

421 

00*075 

28 

33 

846047 

214 

852869 

207 

993178 

421 

006823 

27 

34 

846175 

214 

852745 

207 

993430 

421 

006570 

26 

35 

846304 

214 

852620 

207 

993683 

421 

006317 

25 

36 

846432 

213 

852496 

208 

993936 

421 

006064 

24 

37 

846560 

213 

852371 

208 

994189 

421 

005811 

23 

38 

846688 

213 

852247 

20S 

994441 

42  i 

005559 

22 

39 

840816 

213 

852122 

208 

994694 

421 

005306 

21 

40 

846944 

213 

851997 

208 

994947 

421 

005053 

20 

41 

9.847071 

213 

9.851872 

208 

9.995199 

421 

10.004801 

19 

42 

847199 

213 

851747 

208 

995452 

421 

004548 

18 

43 

847327 

213 

851622 

208 

995705 

421 

004295 

17 

44 

847454 

212 

851497 

209 

995957 

421 

004043 

16 

45 

847582 

212 

851372 

209 

996210 

421 

003790 

15 

46 

847709 

212 

851246 

209 

996463 

421 

003537 

14 

47 

847836 

212 

851121 

209 

996715 

421 

003285 

13 

48 

847964 

212 

850996 

209 

996968 

421 

003032 

12 

49 

848091 

212 

850870 

209 

997221 

421 

002779 

11 

50 

848218 

212 

850745 

209 

997473 

421 

002527 

10 

51 

9.848345 

212 

9.850619 

209 

9.997726 

421 

10.002274 

9 

52 

848472 

211 

850493 

210 

997979 

421 

002021 

8 

53 

848599 

211 

850368 

210 

998231 

421 

001769 

7 

64 

848726 

211 

850242 

210 

998484 

421 

001516 

6 

55 

848852 

211 

850116 

210 

998737  421 

001263 

5 

56 

848979 

211 

849990 

210 

998989  421 

001011 

4 

57 

849106 

211 

849864 

210 

999242  421 

000758 

3 

58 

843232 

211 

849738 

210 

999495 

421 

000505 

2 

59 

8493591  211 

849611 

210 

999748 

421 

000253 

1 

00 

819485   211 

849435 

210 

10.000000 

421 

000000  0 

Cosine 

Sine   |       Coi-ansf.   |         Taritf.     M. 

45  Dogj-eea. 


A  TRAVERSE  TABLE, 


SHOWING   THE   DIFFERENCE    OF 


LATITUDE  AND  DEPARTURE 


FOR  DISTANCES  BETWEEN  1  AND  100,  AND  FOR  ANGLES 
TO  QUARTER  DEGREES  BETWEEN  1°  AND  90°. 


TRAVERSE    TABLE. 


s 

iDeg. 

iDeg. 

JDeg. 

0 
6T 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1 

1.00 

0.00 

1.00 

0.01 

1.00 

0.01 

i 

2 

2.00 

0.01 

2.00 

0.02 

2.00 

0.03 

2 

3 

3.00. 

0.01 

3.00 

0.03 

3.00 

0.04 

3 

4 

4.001 

0.02 

4.00 

0.03 

4.00 

0.05 

4 

5 

5.00 

0.02 

5.00 

0.04 

5.00 

0.07 

5 

6 

6.00 

0.03 

6.00 

0.05 

6.00 

0.08 

6 

7 

7.00 

0.03 

7.00 

0.06 

7.00 

0.09 

7 

8 

8.00 

0.03 

8.00 

0.07 

8.00 

0.10 

8 

9 

9.00 

0.04 

9.00 

0.08 

9.00 

0.12 

9 

10 

10.00 

0.04 

10.00 

0.09 

10.00 

0.13 

10 

11 

11.00 

0.05 

li.OO 

0.10 

11.00 

0.14 

M 

12 

12.00 

0.05 

12.00 

0.10 

12.00 

0.16 

12 

13 

13.00 

0.06 

13.00 

0.11 

13.00 

0.17 

13 

14 

14.00 

0.06 

14.00 

0.12 

14.00 

0.18 

14 

15 

15.00 

0.07 

15.00 

0.13 

15.00 

0.20 

15 

16 

16.00 

0.07  1 

16.00 

0.14 

16.00 

0.21 

16 

17 

17.00 

0.07 

17.00 

0.15 

17.00 

0.22 

17 

18 

18.00 

0.08 

18.00 

0.16 

18.00 

0.24 

18 

19 

19.00 

0.08 

19.00 

0.17 

19.00 

0.25 

19 

20 

20.00 

0.09 

20.00 

0.17 

20.00 

0.26 

20  • 

21 

21.00 

0.09 

21.00 

0.18 

21.00 

0.27 

.  21 

22 

22.00 

0.10 

22.00 

0.19 

22.00 

0.29 

22 

23 

23.00 

0.10 

23.00 

-  0  .SO 

23.00 

0.30 

23 

24 

24.00 

0.10 

24.00 

0.21 

24.00 

0.31 

24 

25 

25.00 

0.11 

25.00 

0.22 

25.00 

0.33 

25 

26 

26.00 

0.11 

26.00 

0.23 

26.00 

0.34 

26 

27 

27.00 

0.12 

27.00 

0.24 

27.00 

0.35 

27 

28 

28.00 

0.12 

28.00 

0.24 

28.00 

0.37 

28 

29 

29.00 

0.13 

29.00 

0.25 

29.00 

0.38 

29 

30 

30.00 

0.13 

30.00 

0.26 

30.00 

0.39 

30 

31 

31.00 

0.14 

31.00 

0.27 

31.00 

0.41 

31 

32 

32.00 

0.14 

32.00 

0.28 

32.00 

0.42 

32 

33 

33.00 

0.14 

33.00 

0-29 

33.00 

0.43 

33 

34 

34.00 

0.15 

34.00 

0.30 

34.00 

0.45 

34 

35 

35.00 

0.15 

35.00 

0.31 

35.00 

•0.46 

35 

36 

36.00 

0.16 

36.00 

0.31 

36.00 

0.47 

36 

37 

37.00 

0.16 

37.00 

0.32 

37.00 

0.48 

37 

38 

38  .00 

0.17 

38.00 

0.33 

38.00 

0.50 

38 

39 

39.00 

0.17 

39.00 

0.34  li  39.00 

0.51 

39 

40 

40.00 

0.17 

40.00 

0.35 

40.00 

0.52 

40 

41 

41.00 

0.18 

41.00 

0.36 

41.00 

0.54 

41 

42 

42.00 

0.18 

42.00 

0.37 

4.2.00 

0.55 

42 

43 

43.00 

0.19 

43.00 

0.38 

43.00 

0.56 

43 

44 

44.00 

0.19 

44.00 

0.38  l|  44.00 

0.58 

44 

45 

45.00 

0.20 

45.00 

0.39 

45.00 

0.59 

45 

46 

46.00 

0.20 

46.00 

0.40 

46.00 

0.60 

46 

47 

47.00 

0.21 

47.00 

0.41  ||  47.00 

0.62 

47 

48 

48.00 

0.21 

48.00 

0.42  il  48.00 

.  0.63 

48 

49 

49.00 

0.21 

49.00 

0.43 

49.00 

0.64 

49 

60 

50.00 

0.22 

50.00 

0.44 

50.00 

0.65 

50 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

•j 

5 

89|  Deg. 

891  Deg. 

1    89i  Deg. 

P 

TKAVEESE    TABLE. 


3 

it 

>eg. 

1 

Deg. 

II 

mmi^^i^mmmmm 

)eg. 

i 

P 

P 

3 

8 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

51 

51.00 

0.22 

51.00 

0.45 

51.00 

0.67 

51 

52 

52.00 

0.23 

52.00 

0.45 

52.00 

0.68 

52 

53 

53.00 

0.23 

53.00 

0.46 

53.00 

0.60 

53 

54 

54.00 

0.24 

54.00 

0.47 

54.00 

0.71 

54 

55 

55.00 

0.24 

55.00 

0.48 

55.00 

0.72 

55 

56 

56.00 

0.24 

56.00 

0.49 

56.00 

0.73 

56 

57 

57.00 

0.25 

57.00 

0.50 

57.00 

0.75 

57 

58 

58.00 

0.25 

•    58.00 

0.51 

57.99 

0.76 

58 

59 

59.00 

0.26 

59.00 

0.51 

58.99 

0.77 

59 

60 

60.00 

0.26 

60.00 

0.52 

59.99 

0.79 

60 

61 

61.00 

0.27 

61.00 

0.53 

60.99 

0.80 

H 

62 

62.00 

0.27 

62.00 

0.54 

61.99 

0.81 

62 

63 

63.00 

0.27 

63.00 

0.55 

62.99 

0.82 

63 

64 

64.00 

0.28 

64.00 

0.56 

63.99 

0.84 

64' 

65 

65.00 

0.28 

65.00 

0.57 

64.99 

0.85 

65 

66 

"  66.00 

0.29 

66.00 

0.58 

65.99 

0.86 

6*6 

67 

67.00 

0.29 

67.00 

0.58 

66.99 

0.88 

67 

68 

68.00 

0.30 

68.00 

0.59 

67.99 

0.89 

68 

69 

69.00 

0.30 

69.00 

0.60 

68.99 

0.90 

69 

70 

70.00 

0.31 

70.00 

0.61 

69.99 

0.92 

70 

71 

71.00 

0.31 

71.00 

0.62 

70.99 

.0.93 

71 

72 

72.00 

0.31 

72.00 

0.63 

71.99 

0.94 

72 

73 

73.00 

0.32 

73.00 

0.64 

72.99 

0.96 

73 

74 

74.00 

0.32 

74.00 

0.65 

73.99 

0.97 

74 

75 

75.00 

0.33 

75.00 

0.65 

74.99 

0.98 

75 

76 

76.00 

0.33 

76.00 

0.66 

75.99 

0.99 

76 

77. 

77.00 

0.34 

77.00 

0.67 

76.99 

.01 

77 

78 

78.00 

0.34 

78.00 

0.68 

77.99 

.02 

78 

79 

79.00 

0.34 

79.00 

0.69 

78.99 

.03 

79 

80 

80.00 

0.35 

80.00 

0.70 

79.99 

.05 

80 

81 

81.00 

0.35 

81.00 

0.71 

80.99 

.06 

81 

82 

82.00 

0.36 

82.00 

0.72 

81.99 

.07 

82 

83 

83.00 

0.36 

83.00 

0.72 

82.99 

.09 

83 

84 

84.00 

0.37 

84.00 

0.73 

83.99 

.10 

84 

85 

85:00 

0.37 

85.00 

0.74    1 

84.99 

.11 

85 

86 

86.00 

0.38 

86.00 

0.75 

85.99 

.13 

86 

87 

87.00 

0.38 

87.00 

0.76 

86.99 

.14 

87 

88 

88.00 

0.38 

88.00 

0.77 

87.99 

.15 

88 

89 

89  .  00 

0.39 

89.00 

0.78 

88.99  • 

.16 

89 

90 

90.00 

0.39 

90.00 

0.79 

89.99 

.18 

90 

91 

91.00 

0.40 

91.00 

0.79 

90.99 

.19 

91 

92 

92.00 

0.40 

92.00 

0.80 

91.99 

.20 

92 

93 

93.00 

0.41 

93.00 

0.81 

92.99 

.22 

93 

94 

94.00 

0.41 

94.00 

0.82 

93.99 

.23 

94 

95 

yo.OO 

0.41 

95.00 

0.83 

94.99 

.24 

95 

96 

96.00 

0.42 

96.00 

0.84 

95.99 

1.26 

95 

97 

97.00 

(s.42    1 

97'.  00 

0.85 

96.99 

1.27 

97 

98 

98.00 

0.43 

98.00 

0.86 

97.99 

1.28 

98 

99 

99.00 

0.43 

99.00 

0.86 

98.99 

1.30 

99 

100 

100.00 

.   0.44 

100.00 

0.87 

99.99 

1.31 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

.5 
P 

89  ? 

Deg. 

89£1 

>eg. 

89^  I 

)eg. 

1 

TRAVERSE    TABLE. 


G 

5' 

iDeg. 

H  Deg. 

H  De£- 

1|  Deg. 

g? 

C6 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

f 

1.00 

0.02 

1,00 

0.02 

1.00 

0.03 

1.00 

0.03 

1 

s 

2.00 

0.03 

2,00 

0.04 

2.00 

0.05 

2.00 

0.06 

2 

3 

3.00 

0.05 

3.00 

0.07 

3.00 

0.08 

3.00 

0.09 

3 

4 

4.00 

0.07 

4.00 

0.09 

4.00 

0.10 

4.00 

0.12 

4 

5 

5.00 

0.09 

5.00 

o.n 

5.00 

0.13 

5,00 

0.15 

5 

6 

6.00 

0.10 

G.OO 

0.13 

6.00 

0.16 

6.00 

0.18 

6r 

7 

7.00 

0.12 

7.00 

0.15 

7.00 

0.18 

7.00 

0.21 

7 

8 

8.00 

0.14 

8.00 

0.17 

8.00 

0.21 

8.00 

0.25 

8 

9 

9.00 

0.16 

9.00 

0.20 

9.00 

0.24 

9.00 

0.28 

9 

10 

10.00 

0.17 

10.00 

0.22 

10.00 

0.26 

10.00 

0.31 

10 

11 

11.00 

0.19 

11.00 

0.24 

11.00 

0.28 

10.99 

0.34 

11 

12 

12.00 

0.21 

12.00 

0.26 

12.00 

0.31 

11.99 

0.37 

12 

13 

13.00 

0.23 

13.00 

0.28 

13.  00 

0.34 

12.99 

0.40 

13 

14 

14.00 

0.24 

14.00 

0.31 

14.00 

0.37 

13.99 

0.43 

14 

15 

15,00 

0.2& 

15.00 

0.33 

14.99 

0.39 

14.99 

0.46 

15 

16 

16.00 

0.28 

16.00 

0.35 

15.99 

0.42 

15.99 

0.49 

1& 

17 

17.00 

0.30 

17.00 

0.37 

16.99 

0.45 

16.99 

0.52 

17 

18 

18.00 

0.31 

18.00 

0.39 

17.99 

0.47 

17.99 

0.55 

18 

19 

19.00 

0.33 

19.00 

0.41 

18.99 

0.50 

18.99 

0.58 

19 

20 

20.00 

0.35 

20.00 

0.44 

19.99 

0.52 

19.99 

0.61 

20 

21 

21.00 

0.37 

21.00 

0.46 

20.99 

0.55 

20.99 

0-.64 

21 

22 

22.00 

0.33 

21.99 

0.48 

21.99 

0.58 

21.99 

0.67 

22 

23 

23.00 

0.40 

22.99 

0.50 

23.99 

0.60 

22.99 

0.70 

23 

24 

24.00 

0.42 

23.99 

0.52 

23.99 

0.63 

23.99 

0.73 

24 

25 

25.00 

0.44 

24.99 

0.55 

24,99 

0.65 

24.99 

0.76 

25 

20 

26.00 

0.45 

25.99 

0.57 

25.99 

0.68 

25.99 

0.79 

26 

27 

27.00 

0.47 

26.99 

0  59 

26.90 

0.71 

26.99 

0.83 

27 

28 

28.00 

0.49 

27.99 

0.61 

27.99 

0.73 

27.99 

0.86 

28 

29 

29.00 

0.51 

28.99 

0.63 

28.99 

0.76 

28.99 

0.89 

29 

30 

30.00 

0.52 

29.99 

0.65 

29.99 

0.79 

29.99 

0.92 

30 

31 

31.00 

0.54 

30.99 

0.68 

30.99 

0.81 

30.99 

0.95 

31 

32 

32.00 

0.56 

31.99 

0.70 

31.99 

0.84 

31.99 

0.98 

32 

33 

32.99 

0.58 

32.99 

0.72 

32.99 

0.86 

32.98 

1.01 

33 

34 

33.99 

0.59 

33.99 

0.74 

33.99 

0.89 

33.98 

'1.04 

34 

35 

34.99 

0.61 

34.99 

0.76 

34.99 

0.92 

34.98 

1.07 

35 

36 

35.99 

O.H3 

35.99 

0.79 

35.99 

0.94 

35.98 

1.10 

36 

37 

36.99 

0.65 

36.99 

0.81 

36.99 

0.97 

36.98 

1.13 

37 

38 

37.99 

0.66 

37.99 

0.83 

37.99 

0.99 

37.98 

1.16 

38 

39 

38.99 

0.68 

38.99 

0.85 

38.99 

1.02 

38.98 

1.19 

39 

40 

39.99 

0.70 

39.99 

0.87 

39.99 

1.05 

39.98 

1.22 

40 

~41 

40.99 

0.72 

40.99 

0.89 

40.99 

1.07 

40.98 

1.25 

41 

42 

41.99 

0.73 

41.99 

0.92 

41.99 

1.10 

41.98 

1.28 

42 

43 

42.99 

0.75 

42.99 

0.94 

42.99 

1.13 

42.98 

1.31 

43 

44 

43.99 

0.77 

43.99 

0.96 

43.99 

1.15 

43.98 

1.34 

44 

45 

44.99 

0.79 

44.99 

0.98 

44.99 

1.18 

44.98 

1.37 

45 

46 

45.99 

0.80 

45.99 

1.00 

45.99 

1.20 

45.98 

:.*o 

46 

47 

46.99 

0.82 

46.99 

1.03 

46.99 

1.23 

46.98 

1.44 

47 

48 

47.99 

0,84 

47.99 

1.05 

47.98 

1.26 

47.98 

1.47 

48 

49 

48.99 

0.86 

48.99 

1.07 

48.98 

1.28 

48.98 

1.50 

49 

50 

49.99 

0.87 

49.99 

1.09 

49.98 

1.31 

49.98 

1.53 

50 

8* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

LaU 

Dep. 

Lat. 

0." 

o 

^ 

s 

Q 

89  Deg. 

88|  Deg. 

88^  De^.           88*  Deg. 

• 

S 

TRAVERSE    TABLE. 


Distance. 

1  Deg. 

U  Deg. 

H  Deg. 

11  Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

D*p. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.99 

0.89 

50.99 

1.11 

50.98 

.34 

50.98 

1.56 

51 

52 

51.99 

0.91 

51.99 

1.13 

51.98 

.36 

51.98 

1.59 

52 

53 

52.99 

0.92 

52.99 

1.16 

52.98 

.39 

52.98 

1.62 

53 

54 

53.99 

0.94 

53.99 

1.18 

53.98 

.41 

53.97 

1.65 

54 

55 

54.99 

0.96 

54.99 

.20 

54.98 

.44 

54.97 

1.68 

55 

56 

55.99 

0.98 

55.99 

.22 

55.98 

.47 

55.97 

1.71 

56 

57 

56.99 

0.99 

56.99 

.24 

56.98 

.49 

56.97 

1.74 

57 

58 

57.99 

1.01 

57.99 

.27 

57.98 

.52 

57.97 

1.77 

58 

59 

58.99 

1.03 

58.99 

.29 

58.98 

.54 

58.97 

1.80 

59 

60 

59  .  99 

1.05 

59.99 

.31 

59.98 

.57 

59.97 

1.83 

60 

61 

60.99 

1.06 

60.99 

.33 

60.98 

.60 

60.97 

1.86 

61 

62 

61.99 

1.08 

61.99 

.35 

61.98 

.02 

61.97 

1.89 

62 

63 

62.99 

1.10 

62.99 

.37 

62.98 

.65 

62.97 

1.92 

63 

64 

63.99 

1.12 

63.98 

.40 

63.98 

.68 

63.97 

1.95 

64 

65 

64.99 

1.13 

64.98 

.42 

64.98 

.70 

64.97 

1.99 

65 

66 

65.99 

1.15 

65.98 

.44 

85.98 

.73 

65.97 

2.02 

66 

67 

66.99 

1.17 

66.98 

.46 

66.98 

.75 

66.97 

2.05 

67 

68 

67.99 

1.19 

67.98 

.48 

67.98 

.78 

67.97 

2.08 

68 

69 

68.99 

1.20 

68.98 

.51 

68.98 

1.81 

68.97 

2.11 

69 

70 

69.99 

1.22 

69.98 

.53 

69.98 

1.83 

69.97 

2.14 

70 

71 

70.99 

1.24 

70.98 

.55 

70.98 

1.86 

70.97 

2.17 

71 

72 

71.99 

1.26 

71.98 

.57 

71.98 

1.88 

71.97 

2.20 

72 

73 

72.99 

1.27 

72.98 

.59 

72.97 

1.91 

''2.97 

2.23 

73 

74 

73.99 

1.29 

73.98 

.61 

73.97 

1.94 

73.97 

2.26 

74 

75 

74.99 

1.31 

74.98 

.641 

74.97 

1.96 

74.97 

2.29 

75 

76 

75.99 

1.33 

75.98 

.66 

75.97 

1.99 

75.96 

2.32 

76 

77 

76  .  99 

1.34 

76.98 

.68 

76.97 

2.02 

76.96 

2.35 

77 

78 

77.99 

.36 

77.98 

.70 

77,97 

2.04 

77.96 

2.38 

78 

79 

78.99 

.38 

78.98 

.72 

78.97 

2.07 

78.96 

2.41 

79 

80 

79.99 

.40 

79.98 

.75 

79  .  97 

2.09 

79.96 

2.44 

80 

81 

80.99 

.41 

80.98 

.77 

80.97 

2.12 

80.96 

2.47 

81 

82  81.99 

.43 

81.98 

.79 

81.97 

2.15 

81.96 

2.50 

82 

83 

82.99 

.45 

82.98 

.81  1 

82.97 

2.17 

82.96 

2.53 

83 

84 

83.99 

.47 

83.98 

.83 

83.97 

2.20 

83.96 

2.57 

84 

85 

84.99 

.48 

84.98 

.85 

84.97 

2.23 

84.96 

2.60 

85 

86 

85.99 

.50 

85.98 

.88 

85.97 

2.25 

85.96 

2.63 

86 

87 

86  .  99 

.52 

86.98 

.90 

86.97 

2.28 

86  .  96 

2.66 

87 

88 

87.99 

.54 

87.98 

.921 

87.97 

2.30 

87.96 

2.69 

88 

89 

88.99 

.55 

88.98 

.94 

88.97 

2.33 

88  .  96 

2.72 

89 

90 

89.99 

.57 

89.98 

.96 

89.97 

2.36 

89.96 

2.75 

90 

91 

90.99 

.59 

90.98 

1.99 

90.97 

2.38 

90.96 

2.78 

91 

92 

91.99 

.61 

91.98 

2.01 

91.97 

2.41 

91.98 

2.81 

92 

93 

92  .  99 

.62 

92.98 

2.03 

92.97 

2.43 

92.96 

2.84 

93 

94 

93.99 

.64 

93.98 

2.05 

93.97 

2.46 

93.96 

2.87 

94 

95 

94.99, 

.66 

94.98 

2.07 

94.97 

2.49 

94.96 

2.90 

95 

96 

95.99 

.68 

95.98 

2.09 

95.97 

2.51 

95.96 

2.94 

96 

97 

96.99 

.69 

96.98 

2.12 

96.97 

2.54 

96.95 

2.96 

97 

98 

97.99 

1.71 

97.98 

2.14 

97.97 

2.57 

97.95 

2.99 

98 

99 

98.98 

1.73 

98.98 

2.16 

98.97 

2.59 

98.95 

3.02 

99 

100 

99.98 

1.75 

99.98 

2.18 

99.97 

2.62 

99.95 

3.05 

100 

I 

Dep. 

Lat. 

Dep 

•Lat.  ||  Dep. 

Lat. 

Dep.   Lat. 

1 

J 

b 

89  Deg. 

I 
88|  Deg. 

881  Deg. 

884  Deg. 

vi 

a 

0 

Tit  AVERSE    TAKLE. 


o 

2  Deg. 

2J  Deg. 

2£  Deg. 

2J  Deg. 

O 
£ 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

§ 
o 

CD 

B 

f 

I 

1.00 

0.03 

J.OO 

0.04 

1.00 

0.04 

1.00 

0.05 

2 

2.00 

0.07 

2.00 

0.08 

2.00 

0.09 

2.00 

0.10 

2 

p 

3.00 

0.10 

3.00 

0.12 

3.00 

0.13 

3.00 

0.14 

3 

4 

4.00 

0.14 

4.00 

0.16 

4.00 

0.17 

4.00 

0.19 

4 

5 

5.00 

0.17 

5.00 

0.20 

5.00 

0.22 

4.99 

0.24 

5 

6 

6.00 

0.21 

6.00 

0.24 

5.99 

0.26 

5.99 

0.29 

6 

7 

7.00 

0.24 

6.99 

0.27 

6.99 

0.31 

6.99 

0.34 

7 

8 

7.99 

0.28 

7.99 

0.31 

7.99 

0.35 

7.99 

0.38 

8 

9 

8.99 

0.31 

8.  .99 

0.35 

8.99 

0.39 

8.99 

0.43 

9 

10 

9.99 

0.35 

9.99 

0.39 

9.99 

0.44 

9.99 

0.48 

10 

11 

10.99 

0.38 

10.99 

0.43 

10.99 

0.48 

10.99 

0.53 

11 

12 

11.99 

0.42 

11.99 

0.47 

11.99 

0.52 

11.99 

0.58 

12 

13 

12.99 

0.45 

12.99 

0.51 

12.99 

0.57 

12.99 

0.62 

13 

14 

13.99 

0.49 

13.99 

0.55 

13.99 

0.61 

13.98 

0.67 

14 

15 

14.99 

0.52 

14.99 

0.59 

14.99 

0.65 

14.98 

0.72 

15 

16 

15.99 

0.56 

15.99 

0.63 

15.99 

0.70 

15.98 

0.77 

16 

17 

16.99 

0.59 

16.99 

0.67 

16.98 

0.74 

16.98 

0.82 

17 

18 

17.99 

0.63 

17.99 

0.71 

17.98 

0.79 

17.98 

0.86 

18 

19 

18.99 

0.66 

18.99 

0.75 

18.98 

0.83 

18.98 

0.91 

19 

20 

19.99 

0.70 

19.98 

0.79 

19.98 

0.87 

19.98 

0.96 

20 

21 

20.99 

0.73 

20.98 

0.82 

20.98 

0.92 

20.98 

.01 

21 

22 

21.99 

0.77 

21.98 

0.86 

21.98 

0.96 

21.97 

.06 

22 

23 

22.99 

O.bO 

22.98 

0.90 

22  .  98 

1.00 

22.97 

.10 

23 

24 

23.99 

0.84 

23.98 

0.94 

23.98 

1.05 

23.97 

.15 

24 

25 

24.98 

0.87 

24.98 

0.98 

24.98 

1.09 

24.97 

.20 

25 

26 

25.98 

0.91 

25.98 

.02 

25.98 

1.13 

25.97 

.25 

26 

27 

26.98 

0.94 

26.98 

.06 

26.97 

1.18 

26.97 

.30 

27 

28 

27.98 

0.98 

27.98 

.10 

27.97 

1.22 

27.97 

.34 

28 

29 

28.98 

1.01 

28.98 

.14 

28.97 

1.26 

28.97 

.39 

29 

30 

29.98 

1.05 

29.98 

.18 

29.97 

1.31 

29.97 

.44 

30 

31 

30.98 

1.08 

30.98 

.22 

30.97 

1.35 

30.96 

.49 

31 

32 

31.98 

1.12 

31.98 

.26 

31.97 

1.40 

31.96 

.54 

32 

33 

32.98 

1.15 

32.97 

.30 

32.97 

1.44 

32.96 

.58 

33 

34 

33.98 

.19 

33.97 

1.33 

33.97 

1.48 

33.96 

.63 

34 

35 

34.98 

.22 

34.97 

1.37 

34.97 

1  .  53 

34.96 

.68 

35 

36 

35  .  98 

.26 

35.97 

1.41 

35.97 

1.57 

35.96 

.73 

36 

37 

36.98 

.29 

36.97 

1.45 

36.96 

1.61 

36.96 

.78 

37 

38 

37.98 

.33 

37.97 

1.49 

37.96 

1.66 

37.96 

.82 

38 

39 

38.98 

1.36 

38.97 

1.53 

38.96 

1.70 

38.96 

.87 

39 

40 

39.98 

1.40 

39.97 

1.57 

39.96 

1.75 

39.95 

1.92 

40 

41 

40.98 

1.43 

40.97 

1.61 

40.96 

1.77 

40.95 

1.97 

41 

42 

41.97 

1.47 

41.97 

1.65 

41.96 

1.83 

41.95 

2.02 

42 

43 

42.97 

1.50 

42.97 

1.69 

42.96 

1.88 

42.95 

2.06 

43 

44 

43.97 

1.54 

43.97 

1.73 

43.96 

1.92 

43.95 

2.11 

44 

45 

44.97 

1.57 

44.97 

1.77 

44.96 

1.96 

44.95 

.  2.16 

45 

46 

45.97 

1.61 

45.96 

1.81 

45.96 

2.01 

45.95 

2.21 

46 

47 

46.97 

1.64 

46.96 

1.85 

46.96 

2.05 

46.95 

2.25 

47 

48 

47.97 

1.68 

47.96 

1.88 

47.95 

2.09 

47.95 

2.30 

48 

49 

48.97 

1.71 

48.96 

1.92 

48.95 

2.14 

48.94 

2.35 

49 

50 

49.97 

1.74 

49.96 

1.96 

49.95 

2.18 

49.94 

2.40 

50 

OJ 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

S 

C 

1 

C 

88  Deg. 

87|  Deg. 

87^  Deg. 

87i  Deg. 

Q 

TRAVERSE   TABLE. 


2 

2  Deg. 

2*  Deg. 

2£  Deg. 

2|  Deg. 

0 

s. 

i" 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 
n 

9 

51 

50.97 

1.78 

50.96 

2.00 

50.95 

2.22 

50.94 

2.45 

51 

52 

51.97 

1.81 

51.96 

2.04 

51.95 

2.27 

51.94 

2.50 

52 

53 

52.97 

1.85 

52.96 

2.08 

52.95 

2.31 

52.94 

2.54 

53 

54 

53.97 

1.88 

53.96 

2.12 

53.95 

2.36 

53  .  94 

2.59 

54 

55 

54.97 

1.92 

54.96 

2.16 

54.95 

2.40 

54.94 

2.64 

55 

56 

55.97 

1.95 

55.96 

2.20 

55.95 

2.44 

55.94 

2.69 

56 

57 

56.97 

1.99 

56.96 

2.24 

56.95 

2.49 

56  .  93 

2.73 

57 

58 

57.96 

2.02 

57.96 

2.28 

57.94 

2.53 

57.93 

2.78 

58 

59 

58.96 

2.06 

58.95 

2.32 

58.94 

2.57 

58.93 

2.83 

59 

60 

59.96 

2.09 

59.95 

2.36 

59.94 

2.62 

59.93 

2.88 

60 

61 

60.96 

2.13 

60,95 

2.39 

60.94 

2.66 

60.93 

2.93 

61 

62 

61.96 

2.16 

61.95 

2.43 

61.94 

2.70 

61.93 

2.97 

62 

63 

62.96 

2.20 

62.95 

2.47 

62.94 

2.75 

62.93 

3.02 

63 

64 

63.96 

2.23 

63.95 

2.51 

63.94 

2.79 

63.93 

3.07 

64 

65 

64.96 

2.27 

64.95 

2.55 

64.94 

2.84 

64.93 

3.12 

65 

66 

65.96 

2.30 

65.95 

2.59 

65.94 

2.88 

65.92 

3.17 

66 

67 

66.96 

2.34 

66.95 

2.63 

66.94 

2.92 

66.92 

3.21 

67 

68 

67.96 

2.37 

67.95 

2.67 

67.94 

2.97 

67.92 

3.26 

68 

69 

68  .  96 

2.41 

68.95 

2.71 

68.93 

3.01 

68.92 

3.31 

69 

70 

69.96 

2.44 

69.95 

2.75 

69.93 

3.05 

69.92 

3.36 

70 

71 

70.96 

2.48 

70.95 

2.79 

70.93 

3.10 

70.92 

3".  41 

71 

72 

71.96 

2.51 

71.94 

2.83 

71.93 

3.14 

71.92 

3.45 

72 

73 

72.96 

2.55 

72.94 

2.87 

72.93 

3.18 

72.92 

3.50 

73 

74 

73  .  95 

2.58 

73.94 

2.91 

73.93 

3.23 

73.91 

3.55 

74 

75 

74.95 

2.62 

74.94 

2.94 

74.93 

3.27 

74.91 

3.60 

75 

76 

75.95 

2.65 

75.94 

2.98 

75.93 

3.31 

75.91 

3.65 

76 

77 

76.95 

2.69 

76.94 

3.02 

76.93 

3.36, 

76.91 

3.70 

77 

78 

77.95 

2.72 

77.94 

3.06 

77.93 

3.40 

77.91 

3.74 

78 

79 

78.95 

2.76 

78.94 

3.10 

78.92 

3.45 

78.91 

3.79 

79 

80 

79  .  95 

2.79 

79.94 

3.14 

79.92 

3.49 

79.91 

3.84 

80 

81 

80.95 

2.83 

80.94 

3.18 

80.92 

3.53 

80.91 

3.89 

81 

82 

81.95 

2.86 

81.94 

3.22 

81.92 

3.58 

81.91 

3.93 

82 

83 

82  .  95 

2.90 

82.94 

3.26 

82.92 

3.62 

82.90 

3.98 

83 

84 

83.95 

2.93 

83.94 

3.30 

83.92 

3.66 

83.90 

4.03 

84 

85 

84.95 

2.97 

84.93 

3.34 

84.92 

3.71 

84.90 

4.08 

85 

86 

85.95 

3.00 

85.93 

3.38 

85.92 

3.75 

85.90 

4.13 

86 

87 

86.95 

3.04 

86.93 

3.42 

86.92 

3.79 

86.90 

4.17 

87 

88 

87.95 

3.07 

87.93 

3.45 

87.92 

3.84 

87.90 

4.22 

88 

89 

88.95 

3.11 

88.93 

3.49 

88.92 

3.88 

88.90 

4.27 

89 

90 

89  .  95 

3.14 

89.93 

3.53 

89.91 

3.93 

89.90 

4.32 

90 

91 

90.95 

3.18 

90.93 

3.57 

90.91 

3.97 

90.90 

4.37 

91 

92 

91.94 

3.21 

91.93 

3.61 

91.91 

4.01 

91.89 

4.41 

92 

93 

92.94 

3.25 

92.93 

3.65 

92.91 

4.06 

92.89 

4.46 

93 

94 

93.94 

3.28 

93.93 

3.69 

93.91 

4.10 

93.89 

4.51 

91 

95 

94.94 

3.32 

94.93 

3.73 

94.91 

4.14 

94.89 

4.56 

95 

96 

95.94 

3.35 

95.93 

3.77 

95.91 

4.19 

95.89 

4.61 

96 

97 

96.94 

3.39 

96.93 

3.81 

96.91 

4.23 

96.89 

4.65 

97 

98 

97.94 

3.42 

97.92 

3.85 

97.91 

4.27 

97.89 

4.70 

93 

99 

98.94 

3.46 

98.92 

3.89 

98.91 

4.32 

98.89 

4.75 

99 

100 

99.94 

3.49 

99.92 

3.93 

99.91 

4.36 

99.88 

4.80 

100 

1 

Dep. 

Lac. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

| 

5 

88  Deg. 

87|  Deg. 

87£  Deg. 

87i  Deg. 

a 

TRAVERSE    TABLE. 


c 

3  Deg. 

3}  Deg. 

3^  Deg. 

3|  Deg. 

O 

1 

i   £?• 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

°ep-   g 

i 

1.00 

0.05 

1.  00 

0.06 

1.00 

0.06 

1.00 

0.06 

1 

2 

2.00 

0.10 

2.00 

0.11 

2.00 

0.12 

2.00 

0.13 

2 

3 

3.00 

0.16 

3.00 

0.17 

2.99 

0.18 

2.99 

0.20!   3 

4 

3.99 

0.21 

3.99 

0.23 

3.99 

0.24 

3.99 

0.26i   4 

5 

4.99 

0.26 

4.99 

0.28 

4.99 

0.31 

4.99 

0.33 

5 

6 

5.99 

0.31 

5.99 

0.34 

5.99 

0.37 

5.99 

0.39 

6 

7 

6.99 

0.37 

6.99 

0.40 

6.99 

0.43 

6.99 

0.46 

7 

8 

7.99 

0.42 

7.99 

0.45 

7.99 

0.49 

7.98 

0.52 

8 

9 

8.99 

0.47 

8.99 

0.51 

8.98 

0  .  55 

8.98 

0.59 

9 

10 

9.99 

0.52 

9.98 

0.57 

9.98 

0.61 

9.98 

0.65 

10 

11 

10.98 

0.58 

10.98 

0.62 

10.98 

0.67 

10.98 

0.72 

11 

12 

11.98 

0.63 

11.98 

0.68 

11.98 

0.73 

11.97 

0.78 

12 

13 

12.98 

0.68 

12.98 

0.73 

12.98 

0.79 

12.97 

0.85 

13 

14 

13.98 

0.73 

13.98 

0.79 

13.97 

0.85 

13.97 

0.92 

14 

15 

14.98 

0.79 

14.98 

0.85 

14.97 

0.92 

14.97 

0.98 

15 

16 

15.98 

0.84 

15.97 

0.91 

15.97 

0.98 

15.97 

.05 

16 

17 

16.98 

0.89 

16.97 

0.96 

16.97 

1.04 

16.96 

.11 

17 

18 

17.98 

0.94 

17.97 

1.02 

17.97 

1.10 

17.96 

.18 

18 

19 

18.98 

0.99 

18.97 

1.08 

18.96 

1.16 

18.96 

.24 

19 

20 

19.97 

1.05 

19.97 

1.13 

19.96 

1.22 

19.96 

•   .31 

20 

21 

20  .  97 

1.101 

20.97 

1.19 

20.96 

1.28 

20.96 

.37 

21 

22 

21.97 

1.15 

21.96 

1.25 

21.96 

1.34 

21.95 

.44 

22 

23 

22.97 

1.20 

22.96 

1.30 

22.96 

1.40 

22.95 

.50 

23 

24 

23.97 

1.26 

23.96 

1.36 

23.96 

1.47 

23.95 

.57 

24 

25 

24.97 

1.31 

24.96 

1.42 

24.95 

1.53 

24.95 

.64 

25 

26 

25.96 

.36 

25  .  96 

1.47  J25.95 

1.59 

25.94 

.70 

26 

27 

26.96 

.41 

26.96 

1.53  26.95 

1.65 

26.94 

.77 

27 

28 

27.96 

1.47 

27.95 

1.59 

27.95 

1.71 

27.94 

.83 

28 

29 

28.96 

.52 

28.95 

1.64 

28  .  95 

1.77 

28.94 

.90 

29 

30 

29.96 

.57 

29.95 

1.70 

29.94 

1.83 

29.94 

.96 

30 

31 

30.96 

1.62 

30.95 

1.76 

30.94 

1.89 

30.93 

2.03 

31 

32 

31.96 

1.67 

31.95 

1.81 

31.94 

1.95 

31.93 

2.09 

32 

33 

32.95 

1.73 

32.95 

1.87 

32.94 

2.0] 

32.93 

2.16 

33 

34 

33.95 

1.78 

33.95 

1.93 

33.94 

2.08 

33.93 

2.22 

34 

35 

34.95 

1.83 

34.94 

1.98 

34.93 

2.11 

34.92 

2.29 

35 

36 

35.95 

1.88 

35.94 

2.04 

35.93 

2.20 

35.92 

2.35 

36 

37 

36  .  95 

1.94 

36.94 

2.10 

36.93 

2.26 

36.92 

2.42 

37 

38 

37.95 

1.99 

37.94 

2.15 

37.93 

2.32 

37.92 

2.49 

38 

39 

38.95 

2.04 

38.94 

2.21 

38.93 

2.38 

38.92 

2.55 

39 

40 

39.95 

2.09 

39.94 

2.27 

39.93 

2.44 

39.91 

2.62 

40 

41 

40.94 

2.15 

40.93 

2.32  i 

40.92 

2.50 

40.91 

2.68 

41 

42 

41.  &4 

2.20 

41.93 

2.38 

41.92 

2.56 

41.91 

2.75 

42 

43 

42.94 

2.25 

42.93 

2.44 

42.92 

2.63 

42.91 

2.81 

43 

44 

43.94 

2.30 

43.93 

2.49 

43.92 

2.69 

43.91 

2.88 

44 

45 

44.94 

2.36 

44.93 

2.55 

44.92 

2.75 

44.90 

2.94 

45 

46 

45.94 

2.41 

45.93 

2.61 

45.91 

2.81 

45.90 

3.01 

46 

47 

46.94 

2.46 

46  .  92 

2.66 

46.91 

2.87 

46.90 

3.07 

47 

48 

47.93 

2.51 

47.92 

2.72 

47.91 

2.93 

47.90 

3.14 

48 

49 

48.93 

2.56 

48.92 

2.78 

48.91 

2.99 

48.90 

3.20 

49 

50 

49.93 

2.62 

49.92 

2.83 

49.91 

3.05 

49.89 

3.27 

50 

I 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

d 

5 

87  Deg. 

86|  Deg. 

86£  Deg. 

86*  Deg. 

s 

TRAVERSE    TAULE. 


p 

3  Deg. 

3}  Deg. 

31  Deg. 

3|  Deg. 

a 

p 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

CD 

51 

50.93 

2.67 

50.92 

2.89 

50.90 

3.11 

50.89 

3.34 

51 

52 

51.93 

2.72 

51.92 

2.95 

51.90 

3.17 

51.89 

3.40)  52 

53 

52.93 

2.77 

52.91 

3.00 

52.90 

3.24 

52.89 

3.47 

52 

54 

53.93 

2.83 

53.91 

3.06 

53.90 

3.30 

53.88 

3,53 

54 

65 

54.92 

2.88 

54.91 

3.12 

54.90 

3.36 

54.88 

3.60 

55 

56 

55.92 

2.93 

55.91 

3.17 

55.90 

3.42 

55.88 

3.66 

56 

57 

56.92 

2.98 

56.91 

3.23 

56.89 

3.48 

56.88 

3  73 

57 

58 

57.92 

3.04 

57.91 

3.29 

57.89 

3.54 

57.88   3.79 

58 

59 

58.92 

3.09 

58.91 

3.34 

58.89 

3.60 

58-87   3.86 

59 

60 

59.92 

3.14 

59.90 

3.40 

59.89 

3.66 

59.87 

3.92 

60 

61 

60.92 

3.19 

60.90 

3.46 

60.89 

3.72 

60.87 

3.99 

61 

62 

6J.92 

3.24 

61.90 

3.51 

61.88 

3.79 

61.87 

4.05 

62 

63 

62.91 

3.30 

62.90 

3.57 

62.88 

3.85 

62,87 

4.12 

63 

64 

63.91 

3.35 

63.90 

3.63 

63.88 

3.91 

63.86 

4.19 

64 

65 

64.91 

3.40 

64.90 

3.69 

64.88 

3.97 

64.86 

4.25 

65 

60 

65.91 

3.45 

65.89 

3.74 

65.88 

4.03 

65.86 

4.32 

66 

67 

66.91 

3.51 

66.89 

3.80 

66.88 

4  09 

66.86 

4.38 

67 

68 

67.91 

3.56 

67.89 

3.86 

67.87 

4.15 

67.85 

4.45 

68 

69 

68.91 

3.61 

68.89 

3.91 

68.87 

4.21 

68.85 

4.51 

69 

70 

69.90 

3.66 

69.89 

3.97 

69.87 

4.27 

69.85 

4.58 

70 

71 

70.90 

3.72 

70.89 

4.03 

70.87   4.33 

70.85 

4.64 

71 

72 

71.90 

3.77 

71.88 

4.08 

71.87   4.40 

71.85 

4.71 

72 

73 

72.90 

3.82 

72.88 

4.14 

72.86 

4.46 

72.84 

4.77 

73 

74 

73.90 

3.87 

73.88 

4.20 

73.86 

4.52 

73.84 

4.84 

74 

75 

74  .  90 

3.93 

74.88 

4.25 

74.86   4.58 

74.84 

4.91 

75 

76 

75.90 

3.98 

75.88 

4.31 

75  861  4.64 

75.84 

4.97 

76 

77 

76.89 

4.03 

76.88 

4.37 

76.86 

4.70 

76.84 

5.04 

77 

78 

77.89 

4.08 

77.87 

4.42 

77.85 

4.76 

77.83 

5.  JO 

78 

79 

78.89 

4.13 

78.87 

4.48 

78.85 

4.82 

78.83 

5.17 

79 

80 

79.89 

4.19 

79.87 

4.54 

79.85 

4.88 

79.83 

5.23 

80 

81 

80.89 

4.24 

80.87 

4.5ft 

80.85 

4.94 

80.83 

5.30 

81 

82 

81.89 

4.29 

81.87 

4.66 

81.85 

5.01 

81.82 

5.36 

82 

83 

82.89 

4.34! 

82.87 

4.71 

82.85 

5.07 

82.82 

5.43 

83 

84 

83.88 

4.40; 

83.86 

4  76 

83.84 

5.13 

83.82 

5.49 

84 

85 

84.88 

4.45 

84.86 

4.82 

84.84 

5.19 

84.82 

5.56 

85 

86 

85.88 

4.50|  85.86 

4  88 

85.84 

5.25 

85.82 

5  .  62 

86 

87 

86.88 

4.55||  86.86 

4.93 

86.84 

5.31 

80.81 

5.69 

87 

88 

87.88 

4.61  !  87.86   4.99 

87.84 

5.37 

87.81 

5.76 

88 

89 

88.88 

4.66  !  88.86   5.05 

88.83 

5.43 

88.81 

5.82 

89 

90 

89.88 

4.71  |!  89.86 

5.10 

89.83 

5.49 

89.81 

5.89 

90 

91 

90.88 

4.^6  il  90.85 

o  .  1  6 

90.83 

5.56 

90.81 

5.95 

91 

92 

91.87 

4.81  !  91.85 

5.22 

91.83 

5.62 

91.80 

6.02 

92 

93 

92.87 

4.871  92.85 

5.27 

92.83 

5.68 

92.80 

6.08 

93 

94 

93.87 

4.92,  93.8.5 

5.33 

93.82 

5.74 

93.80 

6.15 

94 

95 

94.87 

4.97  94.85 

5.39 

94.82 

5.80 

94.80 

6.21 

95 

96 

95.87 

5.02JJ  95.85 

5.44 

95.82 

5.86 

95  .  79 

6.28 

96 

97 

96.87 

5.08 

96.84 

5.50 

96.82 

5.92 

96.79 

6.34 

97 

98 

97.87 

5.13 

97.84 

5.56 

97.82 

5.98 

97.79 

6.41 

98 

99 

98.86 

5.18 

98.84 

5.61 

98.82 

6.04 

98.79 

6.47 

99 

100  99.86 

5.23 

99.84 

5.67 

99.81 

6.10 

99.79 

6.54 

100 

s 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

c 

/  c 

eJ 

2 

87  Deg. 

861  Deg. 

8G|  Deg. 

86}  Deg. 

fi 

5 

10 


TRAVERSE    TABLE. 


* 

4  Deg. 

4}  Deg. 

4-2  Deg. 

4|  Deg. 

1 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

I 

1.00 

0.07 

1.00 

0.07 

1.00 

o.osl 

1.00 

0.08 

1 

2 

2.00 

0.14 

1.99 

0.15 

1.99 

0.16 

1.99 

0.17 

2 

3 

2.99 

0.21 

2.99 

0.22 

2.99 

0.24 

2.99 

0.25 

3 

4 

3.99 

0.28 

3.99 

0.30 

3.99 

0.31. 

3.98 

0.33 

4 

5 

4.99 

0.35 

4.99 

0.37 

4.98 

0.39 

4.98 

0.41 

5 

6 

5.99 

0.42 

5.98 

0.44 

5.98 

0.47 

5.98 

0.50 

6 

7 

6.98 

0.49 

6.98 

0.52 

6.98 

0.55 

6.97 

0.58 

7 

8 

7.98 

0.56 

7.98 

0.59 

7.98 

0.63 

7.97 

0.66 

8 

9 

8.98 

0.63 

8.98 

0.67 

8.97 

0.71 

8.97 

0.75 

9 

10 

9.98 

0.70 

9.97 

0.74 

9.97 

0.78 

9.97 

0.83 

10 

11 

10.97 

0.77 

10.97 

6.82  1 

10.97 

0.86 

0.96 

O.S1 

11 

12 

11.97 

0.84 

11.97 

0.89 

11.96 

0.94 

1.96 

0.99 

12 

13 

12.97 

0.91 

12.96 

0.96 

12.96 

1.02 

2.96 

1.08 

13 

14 

13.97 

0.98 

13.96 

1.C4 

13.96 

1.10 

3.95 

1.16 

14 

15 

14.96 

1.05 

14.96 

1.11 

14.95 

1.18 

4.95 

1.24 

15 

16 

15.96 

.12 

15.96 

1.19 

15.95 

1.26 

15.95 

1.32 

16 

17 

16.96 

.19 

16.95 

1.26 

16.95 

1.33 

16.94 

1.41 

17 

18 

17.96 

.26 

17.95 

1.33 

17.94 

1.41 

17.94 

1.49 

18 

19 

18.95 

.33 

18.95 

1.40 

18.94 

1.49 

18.93 

1.57 

19 

20 

19.95 

.40 

19.95 

1.48 

19.94 

1.57 

19.93 

1.66 

20 

21 

20.95 

.46 

20.94 

1.56 

20.94 

1.651 

20.93 

1.74 

21 

22 

21.95 

.53 

21.94 

1.63. 

21.93 

1.73 

21.92 

1.82 

22 

23 

22.94 

.60 

22.94 

1.70 

22.93 

1.80 

22.92 

1.90 

23 

24 

23.94 

.67' 

23.93 

1.78 

23.93 

1.88 

23.92 

1.99 

24 

25 

24.94 

.74 

24.93 

1.85 

24.92 

1.96 

24.91 

2.07 

25 

26 

25.94 

1.81 

25.93 

1.93 

25.92 

2.04 

25.91 

2.15 

26 

27 

26.93 

1.88 

26.93 

2.00 

26.92 

2.12 

26.91 

2.24 

27 

28 

27.93 

1.95 

27.92 

2.08 

27.91 

2.20 

27.90 

2.32 

28 

29 

28.93 

2.02 

28.92 

2.15 

28.91 

2.28 

28.90 

2.40 

29 

30 

29.93 

2.09 

29.92 

2.22 

29.91 

2.35 

29.90 

2.48 

30 

31 

30.92   2.16 

30.91 

2.30 

30.90 

2.43 

30.89 

2.57 

31 

32 

31.92   2.23 

31.91 

2.37 

31.90 

2.51 

31.89 

2.65 

32 

33 

32.92   2.30 

32  .  9  1 

2.45 

32.90 

2.59 

32.89 

2.73 

33 

34 

33.92|  2.37 

33.91 

2.52 

33.90 

2.67 

33.88 

2.82 

34 

35 

34.91 

2.44 

34.90 

2.59 

34.89 

2.75 

34.88 

2.90 

35 

36 

35.91 

2.51 

35.90 

2  .  07 

35.89 

2.82 

35.88 

2.98 

36 

37 

36.91 

2.58 

36.90 

2.74 

36.89 

2.90 

36.87 

3.06 

37 

38 

37.91  I  2.65 

37  .  90 

2.82 

37.88 

2.98 

37.87 

3.15 

38 

39 

38.90   2.72 

38.89 

2.89 

38.88 

3.06 

38.87 

3.23 

39 

40 

39.90;  2.79 

39.89 

2.96 

39.88 

3.14 

39.86 

3.31 

40 

41 

40.90,  2.86 

40.89 

3.04i  40.87 

3.22 

40.86 

3.40 

41 

42 

41.90   2.93 

41.88 

3.11 

41.87 

3.30 

41.86 

3.48 

42 

43 

42.90   3.00 

42.88 

3.19 

42.87 

3.37 

42.85 

3.56 

43 

44 

43.89,  3.07 

43.88 

3.26 

43.86 

3.45 

43.85 

3.64 

44 

45 

44.89   3.14 

44.88 

3.33 

44.86 

3.53 

44.85 

3.73 

45 

46 

45.89   3.21 

45.87 

3.41 

45.86 

3.61 

45.84 

3.81 

46 

47 

46.89   3.28 

46.87 

3.48 

46.86 

3.69 

46.84 

3.89 

47 

48 

47.88   3.35 

47.87 

3.56 

47.80 

3.77 

47.84 

3.97 

48 

49 

48.88   3.42 

48.87 

3.63 

48.85 

3.84 

48.83 

4.06 

49 

50 

49.88 

3.49 

49.86 

3.71 

49.85 

3.92 

49.83 

4.14 

50 

I 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

.9 
P 

86  Deg. 

85f  Deg. 

85*  Deg. 

85i  Deg. 

1 

TRAVERSE    TABLE. 


11 


•G 

4  Deg. 

4J  Deg. 

4i  Deg. 

4|  Deg. 

C 

I 

I 

a 
o 
o 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

§ 

51 

50.88 

3.56 

50.86 

3.78 

50.84 

4.00 

50.82 

4.22 

51 

52 

51.87 

3.63 

51.86 

3.85 

51.84 

4.08 

51.82 

4.31 

52 

53 

52.87 

3.70 

52.85 

3.93 

52.84 

4.16 

52.82 

4.39 

53 

54 

53.87 

3.77 

53.85 

4.00 

53.83 

4.24 

53.81 

4.47 

54 

55 

54.87 

3.84 

54.85 

4.08 

54.83 

4.32 

54.81 

4.55 

55 

56 

55.86 

3.91 

55.85 

4.15 

55.83 

4.39 

55.81 

4.64 

56 

57 

56  .  86 

3.08 

56.84- 

4.22 

56.82 

4.47 

56.80 

4.72 

57 

58 

57.86 

4.05 

57.84 

4.30 

57.82 

4.55 

£7.80 

4.80 

58 

59 

58.86 

4.12 

58.84 

4.37 

58.82 

4.63 

58.80 

4.89 

59 

60 

59.85 

4.19 

59.84 

4.45 

59.82 

4.71 

59.79 

4.97 

60 

61 

60.85 

4.26 

60.83 

4.52 

60.81 

4.79 

60.79 

"5.05" 

61 

62 

61.85 

4.32 

61.83 

4.59 

61.81 

4.86 

61.79 

5.13 

62 

63 

62.85 

4.39 

62.83 

4.67 

62.81 

4.94 

62  .  78 

5.22 

63 

64 

63.84 

4.46 

63.82 

4.74 

63.80 

5.02 

63.78 

5.30 

64 

65 

64.84 

4,  53 

64.82 

4.82 

64.80 

5.10 

64.78 

5.38 

65 

66 

65.84 

4.60 

65.82 

4.89 

65.80 

5.18 

65.77 

5.47 

66 

67 

06.  84 

4.67 

66.82 

4.97 

66.79 

5.26 

66  .  77 

5.55 

67 

68 

67.83 

4.74 

67.81 

5.04 

67.79 

5.34 

67.77 

5.63 

68 

69 

68.83 

4.81 

68.81 

•5.11 

68.79 

5,41 

68  .  76 

5.71 

69 

70 

69.83 

4.88 

69.81 

6.19 

69.78 

5.49 

69,76 

5.80 

70 

71 

70.83 

4.95 

70.80 

5.26 

70.78 

5.57 

70  .  76 

5.88 

71 

72 

71.82 

5.02 

71.80 

5.34 

71.78 

5.65 

71.75 

5.98 

72 

73 

72.82 

5.09 

72.80 

5.41 

72.77 

5.73 

72.75 

6.04 

73 

74 

73.82 

5.16 

73.80 

5.48 

73.77 

5.81 

73.75 

6.13 

74 

75 

74.82 

5.23 

74.79 

5.56 

74.77 

5.88 

74.74 

6.21 

75 

76 

75.81 

5.30 

75.79 

5.63 

75.77 

5.96 

75  .  74 

6.29 

76 

77 

76.81 

5.37 

76.79 

5.71 

76.76 

6.04 

76.74 

6.38 

77 

78 

77.81 

5.44 

77.79 

5.78 

77.76 

6.12 

77.73 

6.46 

78 

79 

78.81 

5.51 

78.78 

5.85 

78.76 

6.20 

78.73 

6.54 

79 

80 

79.81 

5.58 

79.78 

5.93 

79.75 

6.28 

79.73 

6.62 

8-0 

81 

80.80 

5.65 

80.78 

6.00 

80  .  75 

6.36 

80  .  72 

6.71 

81 

82 

81.80 

5.72 

81.78 

6.08 

81.75 

6.43 

81.72 

6.79 

82 

83 

82.80 

5.79 

82.77 

6.15 

82.74 

6.51 

82.71 

6.87 

83 

84 

83.80 

5.86 

83.77 

6.23 

83.74 

6.59 

83.71 

6.96 

84 

85 

84.79 

5.93 

84.77 

6.30 

84.74 

6.67 

84.71 

7.04 

85 

86 

85.79 

6.00 

85.76 

6.37 

8,->.  73 

6.75 

85.70 

7.12 

86 

87 

86.79 

6.07 

86.76 

6.45 

86.73 

6.83 

86.70 

7.20 

87 

88 

87.79 

6.14 

87.76 

6  .  52 

87.73 

6.90 

87.70 

7.29 

88 

89 

88.78 

6.21 

88.76 

6.60 

88.73 

6.98 

88.70 

7.37 

89 

90 

89.78 

6.28 

89.75 

6.67 

89.72 

7.06 

89.69 

7.45 

90 

91 

90.78 

6.35 

90.75 

6.74 

90.72 

7.14 

90.69 

7.54 

91 

92 

91.78 

6.42  ! 

91.75 

6.82 

91.72 

7.22 

91.68 

7.62 

92 

93 

92.77 

6.49 

92.74 

6.89 

92.71 

7.30 

92.68 

7.70 

93 

94 

93.77 

6.56 

93.74 

6.97 

93.71 

7.38 

93.68 

7.78 

94 

95 

94.77 

6.63 

94.74 

7.04 

94.71 

7.45 

94.67 

7.87 

95 

96 

95.77 

6.70 

95.74 

7.11 

95.70 

7.53 

95.67 

7.95 

96 

97 

96.76 

6.77 

96.73 

7.  IS 

96.70 

7.61 

96.67 

8.03 

97 

98 

97.76 

6.84 

97.73 

7.26 

97.70 

7.69 

97.66 

8.12 

98 

99 

98.76 

6.91 

98.73 

7.34 

98.69 

7.77 

98.66 

8.20 

99 

100 

99.76 

6.98 

99.73 

7.41 

99.69 

7.85 

99.66 

8.28 

100 

'  0 

o 
ft 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

"rt 

5 

86  Deg. 

85|  Deg. 

85£  Deg. 

85i  Deg. 

Q 

TKAVERSE    TABLE. 


!~u-u 

b 

S- 

Eo 

5  Deg. 

5{  Deg. 

51  Deg. 

5|  Deg. 

D 
& 

P 

5 

o 

ro 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

1 

1.00 

0.09 

1.00 

0  .  09 

1.00 

0.10 

0.99 

0.10 

1 

2 

1.99 

0.17 

1.99 

0.18 

1.99 

0.19 

1.99 

0.20 

2 

3 

2.99 

0.28 

2.99 

0.27 

2.99 

0.29 

2.98 

0.30 

3 

4 

3.98 

0.35 

3,98 

0.37 

3.98 

0.38 

3.98 

0.40 

4 

5 

4.98 

0.44 

4.98 

0.46 

4.98 

0.48 

4.97 

0.50 

5 

6 

5  .  98 

0.52 

5.97 

0.55 

5.97 

0.58 

5.97 

0.60 

6 

7 

6.97 

0.61 

6.97 

0.64 

6.97 

0.67 

6.96 

0.70 

7 

8 

7.97 

0.70 

7.97 

0.73 

7.96 

0.76 

7.96 

0.80 

8 

9 

8.97 

0.78 

8.98 

0.82 

8  96 

0.86 

8.95 

0.90 

9 

10 

9.96 

0.87! 

9.96 

0.92 

9.95 

0.96 

9.95 

1.00 

10 

11 

10.96 

0.96! 

10.95 

1.  01 

10.95 

1.05 

10.94 

1.10 

11 

12 

1  1  .  95 

1.05 

11.95 

1.10 

11.94 

1.15 

1  1  .  94 

1.20 

12 

13 

12.95 

1.13 

12.95 

1.19 

12.94 

1.25 

12.93 

1.30 

13 

14 

13.95 

1.22 

13.94 

1.28 

13.94 

1.34 

13.93 

1.40 

14 

15 

14.94 

1.31 

14.94 

1.37 

14.93 

1.44 

14.92 

1.50 

15 

16 

15.94 

1.39 

15.93 

1.46 

15.93 

1.53 

15.92 

1.60 

16 

17 

16.94 

1.48 

16.93 

1.56 

16.92 

1.63 

16.91 

1.70 

17 

18 

17.93 

1.57 

17.92 

1.65 

17.92 

1.73 

17.91 

1.80 

18 

19 

18.93 

1.66 

18.92 

1.74 

18.91 

1.82  1 

18.90 

1.90 

19 

20 

19.92 

1.74 

19.92 

1.83 

19.91 

1.92  | 

19/90 

2.00 

20 

21 

20.92 

1.83 

20.91 

1.92 

20.90 

2.01  1 

20.89 

2.10 

21 

22 

21.92 

1.92 

21.91 

2.01 

21.90 

2.11 

21.89 

2.20 

22 

23 

22.91 

2.00< 

22.90 

2.10 

22.89 

2.20 

22.88 

2.30 

23 

24 

23.91 

2.09 

23.90 

2.20 

23.89 

2.30 

23.88 

2.40 

24 

25 

24.90 

2.18 

24.90 

2.29 

24.88 

2.40 

24.87 

2.50 

25 

26 

25.90 

2.27 

25.89 

2.38 

25.88 

2.49 

25.87 

2.60 

26 

27 

26.90 

2.35 

26.89 

2.47 

26.88 

2.59 

26.86 

2.  .71 

27 

28 

27.89 

2.44 

27.88 

2.56 

27.87 

2.88 

27.86 

2.81 

28 

29 

28.89 

2.53 

28.88 

2.65 

28.87 

2.78 

28  .  85 

2.91 

29 

30 

29.89 

2.61 

29.87 

2.75 

29.86 

2.88 

29.85 

3.01 

30 

31 

30.88 

2.70 

30.87 

2.84 

30.86 

2.97 

30.84 

3.11 

31 

32 

31.88 

2.79 

31.87 

2.93 

31.85 

3.07 

31.84 

3.21 

32 

33 

32.87 

2.88 

32.86 

3.02 

32.85 

3.16 

32.83 

3.31 

33 

34 

33.87 

2.96 

33.86 

3.11 

33  .  84 

3.26 

33.83 

3.41 

34 

35 

34.87 

3.05 

34.85 

3  .  20 

34.84 

3.35 

34.82 

3.51 

35 

36 

35.86 

3.14 

35.85 

3.29 

35.83 

3.45 

35.82 

3.61 

36 

37 

36  .  86 

3.22 

38.84 

3.39 

36.83 

3.55 

36.81 

3.71 

37 

38 

37.86 

3.31 

37.84 

3.48 

37  .  83 

3.64 

37.81 

3.81 

38 

39 

38.85 

3.40 

38.84 

3.57 

38.82 

3.74 

38.80 

3.91 

39 

40 

39.85 

3.49 

39.83 

3.66 

39.82 

3.83 

39.80 

4.01 

40 

41 

40.84 

3.57 

|40.83 

3.75 

40.81 

3.93 

40.79 

4.J1 

41 

42 

41.84 

3.66 

41.82 

3.84 

41.81 

4.03 

41.79 

4.21 

42 

43 

42.84 

3.75 

42.82 

3.93 

42.80 

4.12 

42.78 

4.31 

43 

44 

43.83 

3.83 

43.82 

4.03 

43.80 

4.22 

43.78 

4.41 

44 

45 

44.83 

3.92 

44.81 

4.12 

44.79 

4.31 

44.77 

4.51 

45 

46 

45.82 

4.01 

45.81 

4.21 

45.79 

4.41 

45.77 

4.61 

46 

47 

46.82 

4.10 

46.80 

4.30 

46.78 

4.50 

46.76 

4.71 

47 

48 

47.82 

4.18 

47.80 

4.39 

47.78 

4.60 

47.76 

4.81 

48 

49 

48.81 

4.27 

48.79 

4.48 

48.77 

4.70 

48.75 

4.91 

49 

50 

49.81 

4.36 

49.79 

4.58 

49.77 

4.79 

49.75 

5.01 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Q> 

aj 
"en 

5 

85  Deg. 

84|  Deg. 

841  Deg. 

84i  Deg. 

1 

Q 

i 

TRAVERSE    TABLE. 


13 


? 

5  Deg. 

5|  Deg. 

5|  Deg. 

5|  Deg. 

1 

I 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

51 

50.81 

4.44 

50.79 

4.67 

50.77 

4.89 

50.74 

5.11 

51 

52 

51.80 

4.53 

51.78 

4.76 

51.76 

4.98 

51.74 

5.21 

52 

53 

52.80 

4.62 

52.78 

4.85 

52.76 

5.08 

52.73 

5.31 

53 

54 

53.79 

4.71 

53.77 

4.94 

53.75 

5.18 

53.73 

5.41 

54 

55 

54.79 

4.79 

54.77 

5.03 

54.75 

5.27 

54.72 

5.51 

55 

56 

55.79 

4.88 

55.77 

5.12 

55.74 

5.37 

55.72 

5.61 

56 

57 

56.78 

4.97 

56.76 

5.22 

56.74 

5.46 

56.71 

5.71 

57 

58 

57.78 

5.06 

57.76 

5.31 

57.73 

5.56 

57.71 

5.81 

58 

69 

58.78 

5.14 

58.75 

5.40 

58.73 

5.65 

58.70 

5.91 

59 

60 

59.77 

5.23 

59.75 

5.49 

59.72 

5.75 

59.70 

6.01 

60 

61 

60.77 

5.32 

60.74 

5.58 

60.72 

5.85 

60.69 

6.11 

61 

62 

61.76 

5.40 

61.74 

5.67 

61.71 

5.94 

61.69 

6.21 

62 

63 

62.76 

5.49 

62.74 

5.76 

62.71 

6.04 

62.68 

6.31 

63 

64 

63.76 

5.58 

63.73 

5.86 

63.71 

6.13 

63.68 

6.41 

64 

65 

64.75 

5.67 

64.73 

5.95 

64.70 

6.23 

64.67 

6.51 

65 

66 

65.75 

5.75 

65.72 

6.04 

65.70 

6.33 

65.67 

6.61 

66 

67 

66.75 

5.84 

66.72 

6.13 

66.69 

6.42 

66.66 

6.71 

67 

G'8 

67.74 

5.93 

67.71 

6.22 

67.69 

6.52 

67.66 

6.81 

68 

G9 

68.74 

6.01 

68.71 

6-31 

68.68 

6.61 

68.65 

6.91 

69 

70 

69.73 

6.10 

69.71 

6  41 

69.68 

6.71 

69.65 

7,01 

70 

71 

70.73 

6.19 

70.70 

6  50 

70.67 

6.81 

70.64 

7.11 

71 

52 

71.73 

6.28 

71.70 

6  59 

71.67 

6.90 

71.64 

7.21 

72 

73 

72.72 

6.36 

72.69 

6  68 

72.66 

7.00 

72.63 

7.31 

73 

•4 

73.72 

6.45 

73.69 

6  77 

73.66 

7.09 

73.63 

7.41 

74 

75 

74.71 

6.54 

74.69 

6^86 

74.65 

7.19 

74.62 

7.51 

75 

76 

75.71 

6.62 

75.68 

6  95 

75.65 

7.28 

75.62 

7.61 

76 

77 

76.71 

6.71 

76.68 

7.05 

76.65 

7.38 

76.61 

7.71 

77 

78 

77.70 

6.80 

77.67 

7-14 

77.64 

7.48 

77.61 

7.81 

78 

79 

78.70 

6.89 

78.67 

7  23 

78.64 

7.57 

78.60 

7.91 

79 

80, 

79.70 

6.97 

79.66 

7  32 

79.63 

7.67 

79.60 

8.02 

80 

81 

80.69 

7.06 

80.66 

7  41 

80.63 

7.76 

80.59 

8.12 

81 

82 

81.69 

7.15 

81.66 

7  50 

81.62 

7.86 

81.59 

8.22 

82 

83 

82.68 

7.23 

82.65 

7  59 

82.62 

7.96 

82.58 

8.32 

83 

84 

83.68 

7.32 

83.65 

7-69 

83.61 

8.05 

83.58 

8.42 

84 

85 

84.68 

7.41 

84.64 

7.78 

84.61 

8.15 

84.57 

8.52 

85 

86 

85.67 

7.50 

85.64 

7.87 

85.60 

8.24 

85.57 

8.62 

86 

87 

86.67 

7.58 

86.64 

7.96 

86.60 

8.34 

86.56 

8.72 

87 

88 

87.67 

7.67 

87.63 

8.05 

87.59 

8.43 

87.56 

8.82 

88 

89 

88.66 

7.76 

88.63 

8.14 

88.59 

8.53 

88.55 

8.92 

89 

90 

89.66 

7.84 

89.62 

8.24 

89.59 

8.63 

89.55 

9.02 

90 

91 

90.65 

7.93 

90.62 

8.33 

90.58 

8.72 

90.54 

9.12 

91 

92 

91.65 

8.02 

91.61 

8.42 

91.58 

8.82 

91.54 

9.22 

92 

93 

92.65 

8.11 

92.61 

S.51 

92.57 

8.91 

92.53 

9.32 

93 

94 

93.64 

8.19 

93.61 

3.60 

93.57 

9.01 

93.53 

9.42 

94 

95 

94.64 

8.28 

94.60 

9.69 

94.56 

9.11 

94.52 

9.52 

95 

96 

95.63 

8.37 

95.60 

8.78 

95.56 

9.20 

95.52 

9.62 

96 

97 

96.63 

8.45 

96.59 

8.88 

96.55 

9.30 

96.51 

9.72 

97 

98 

97.63 

8.54 

97.59 

8.97 

97.55 

9.39 

97.51 

9.82 

98 

99 

98.62 

8.63 

98.59 

9.06 

98.54 

9.49 

98.50 

9.92 

99 

100 

99.62 

8.72 

99.58 

9.15 

99.54 

9.58 

99.50 

10.02 

100 

I 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

§ 

5 

85  Deg. 

84|  Deg. 

841  Deg. 

844  Deg. 

3 

u 


TRAVERSE    TABLE, 


O 

6  Deg. 

6J  Deg. 

6£  Deg. 

G|  Deg. 

O 

f 

? 
a 
n 

(0 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.99 

0.10 

0.99 

0.11 

0.99 

0.11 

0.99 

~T>TT2~ 

1 

2 

1.99 

0.21 

1.99 

0.22 

1.99 

0.23 

1.99 

0^24 

2 

3 

2.98 

0.31 

2.98 

0.33 

2.98 

0.34 

2-.  98 

0.35 

3 

4 

3.98 

0.41 

3.98 

0.44 

3.97 

0.45 

3.97 

0.47 

4 

5 

4.97 

0.52 

4.97 

0.54 

4.97 

0.57 

4.97 

0.59 

5 

6 

5.97 

0.63 

5.96 

0.65 

5.96 

0.68 

5.96 

0.71 

6 

7 

6.96 

0.73 

6.96 

0.76 

6.96 

0.79 

6.95 

0.82 

7 

8 

7.96 

0.84 

7.95 

0.87 

7.95 

0.91 

7.94 

0.94 

8 

9 

8.95 

0.94 

8.95 

0.98 

8.94 

1.02 

8.94 

.06 

9 

10 

9.95 

1.05 

9.94 

1.09 

9.94 

1.13 

9.93 

.18 

10 

11 

10.94 

1.15 

10.93 

1.20 

10.93 

1.25 

10.92 

.29 

11 

12 

11.93 

1.25 

11.93 

1.31 

11.92 

1.36 

11.92 

.41 

12 

13 

12.93 

1.36 

12.92 

1.42 

12.92 

1.47 

12.91 

.53 

13 

14 

13.92 

1.46 

13.92 

1.52 

13.91 

1.59 

13.90 

.65 

14 

15 

14.92 

1.57 

14.91 

1.63 

14.90 

1.70 

14.90 

.76 

15 

16 

15.91 

1.67 

15.90 

1.74 

15.90 

1.81 

15.89 

.88 

16 

17 

16.91 

1.78 

16.90 

1.85 

16.89 

1.92 

16.88 

2.00 

17 

18 

17.90 

1.88 

17.89 

1  .  96 

17.88 

2.04 

17.88 

2.12 

18 

19 

18.90 

1.99 

18.89 

2.07 

18.88 

2.15 

18.87 

2.23 

19 

20 

19.89 

2.09 

19.88 

2.18 

19.87 

2.26 

19.86 

2.35 

20 

21 

20.88 

2.20 

20.88 

2.29 

20.87 

2.38 

20.85 

2.47 

21 

22 

21.88 

2.30 

21.87 

2.40 

21.86 

2.49 

21.85 

2.59 

22 

23 

22.87 

2.40 

22.86 

2.50 

22.85 

2.60 

22.84 

2.70 

23 

24 

23.87 

2.51 

23.86 

2.61 

23.85 

2.72 

23.83 

2.82 

24 

25 

24.86 

2.61 

24.85 

2.72 

24.84 

2.83 

24.83 

2.94 

25 

26 

25.86 

2.72 

25.85 

2.83 

25.83 

2.94 

25.82 

3.06 

26 

27 

26.85 

2.82 

26.84 

2.94 

26.83 

3.06 

26.81 

3.17 

27 

28 

27.85 

2.93 

27.83 

3.05 

27.82 

3.17 

27.81 

3.29 

28 

29 

28.84 

3.03 

28.83 

3.16 

28.61 

3.28 

28.80 

3.41 

29 

30 

29.84 

3.14 

29.82 

3.27 

29.81 

3.40 

29.79 

3.53 

30 

31 

30.83 

3.24 

30.82 

3.37 

30.80 

3.51 

30.79 

3.64 

31 

32 

31.82 

3.34 

31.81 

3.48 

31.79 

3.62 

31.78 

3.76 

32 

33 

32.82 

3.45 

32.80 

3.59 

32.79 

3.74 

32.77 

3.88 

33 

34 

33.81 

3.55 

33.80 

3.70 

33  .  78 

3.85 

33.76 

4.00 

34 

35 

34.81 

3.66 

34.79 

3.81 

34.78 

3.96 

34.76 

4.11 

35 

36 

35.80 

3.76 

35.79 

3.92 

35.77 

4.08 

35,75 

4.23 

36 

37 

36.80 

3.87 

36.78 

4.03 

36.76 

4.19 

36.75 

4.35 

37 

38 

37.79 

3.97 

37.77 

4.14 

37.76 

4.30 

37.74 

4.47 

38 

39 

38.79 

4.08 

38.77 

4.25 

38  .  75 

4.41 

38.73 

4.58 

39 

40 

39.78 

4.18 

39  .  76 

4.35 

39.74 

4.53 

39.72 

4.70 

40 

41 

40.78 

4.29 

40.76 

4.46 

40  .  74 

4.64 

40.72 

4.82 

41 

42 

41.77 

4.39 

41.75 

4.57 

41.73 

4.76 

41.71 

4.94 

42 

43 

42.76 

4.49 

42.74 

4.68 

42.72 

4.87 

42.70 

5.05 

43 

44 

43.76 

4.60 

43.74 

4.79 

43.72 

4.98 

43.70 

5.17 

44 

45 

44.75 

4.70 

44.73 

4.90 

44.71 

5.09 

44.69 

5.29 

45 

46 

45  .  75 

4.81 

45.73 

5.01 

45.70 

5.21 

45.68 

5.41 

46 

47 

46.74 

4.91 

46.72 

5.12 

46.70 

5.32 

46.67 

5.52 

47 

48 

47.74 

5.02 

47.71 

5.23 

47.69 

5.43 

47.67 

5.64 

48 

49 

48.73 

5.12 

48.71 

5.34 

48.69 

5.55 

48.66 

5.76 

49 

50 

49.73 

5.23 

49.70 

5.44 

49.68 

5.66 

49.65 

5.88 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

In 

b 

84  Deg. 

83|  Deg. 

83  i  Deg. 

83J  Deg. 

.2 

b 

TRAVERSE    TABLE. 


15 


o 

6  Deg. 

64  Deg. 

«iDeg 

6f  Deg. 

y 

tn 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

51 

50.72 

5.33 

50.70 

5.55 

50.67 

5.77 

50.65 

5.99 

51 

52 

51.72 

5,44 

51.69 

5.66 

51.67 

5.89 

M.64 

6.11 

52 

53 

52.71 

5.54 

52.68 

5.77 

52.66 

6.00 

52.63 

6.23 

53 

54 

53.70 

5.64 

53.68 

5.88 

53.65 

6.11 

53.63 

6.35 

54 

55 

54.70 

5.75 

54.67 

5.99 

54.65 

6-23 

54.62 

6.46 

55 

56 

55.69 

5.85 

55.67 

6.10 

55.64 

6.34 

55.01 

6.58 

56 

57 

56.69 

5.96 

56.66 

6.21 

56.63 

6-45 

56.60 

6.70 

57 

58  !57.68 

6.06 

57.66 

6.31 

57.63 

6-57 

57.60 

6.82 

58 

59 

58.68 

6.17 

58.65 

6.42 

'58.62 

6-68 

58.59 

6.93 

59 

60 

59,67 

6.27 

59.64 

6.53 

59.61 

6-79 

59.58 

7.05 

60 

61 

60,67 

6.38 

60.64 

6.64 

60.61 

6.91 

60.58 

7.17 

61 

62 

61.66 

6,48 

61.63 

6.75 

61.60 

V.02 

61.57 

7.29 

62 

63 

62,65 

6.59 

62.63 

6.86 

62  .  60 

7.13 

62.56 

7.40 

63 

64 

63.65 

6,69 

63.62 

6.97 

63.59 

7.25 

63.56 

7.52 

64 

65 

64,64 

6.79 

64.61 

7.08 

64.58 

7.36 

64.55 

7.64- 

65 

66 

65.64 

6.90 

65.61 

7.19 

65.58 

7.47 

65.54 

7.76 

66 

67 

66.63 

7.00 

66.60 

7.29 

66.57 

7  58 

66.54 

7.88 

67 

68 

67.63 

7.11 

67.60 

7.40 

67.56 

7.70 

67.53 

7.99 

68 

69 

68.62 

7.21 

68  .  59 

7.51 

68.56 

7.81 

68.52 

8.11 

69 

70 

69.62 

7.32 

69  .  58 

7.62 

69  .  55 

7.92 

69.51 

8.23 

70 

71 

70.61 

7.42 

70.58 

7.73 

70.54 

8.04 

70.51 

8.35 

71 

72 

71.61 

7.53 

71.57 

7.84 

71.54 

8.15 

71.50 

8.46 

72 

73 

72.60 

7.63 

72.57 

7.95 

72.53 

8.26 

72.49 

8.58 

73 

74 

73.59 

7.74 

73.56 

8.06 

73.52 

8.38 

73.49 

8.70 

74 

75 

74.59 

7.84 

74.55 

8.17 

74.52 

8.49 

74.48 

8.82 

75 

76 

75.58 

7.94 

75.55 

8.27 

75.51 

8.60 

75.47 

8.93 

76 

77 

76.58 

8.05 

76.54 

8.38 

76.51 

8.72 

76.47 

9.05 

77 

78 

77.57 

8.15 

77.54 

8.49 

77.50 

8.83 

77.46 

9.17 

78 

79 

78.57 

8.26 

78.53 

8.60 

78.49 

8.94 

78.45 

9.29 

79 

80 

79.56 

8.36 

79.53 

8.71 

79.49 

9.06 

79.45 

9.40 

80 

81 

80  .  56 

8.47 

80.52 

8.82 

80.48 

9.17 

80.44 

9.52 

81 

82 

81.55 

8.57 

81.51 

8.93 

81.47 

9.28 

81.43 

9.64 

82 

83 

82  .  55 

8.68 

82.51 

9.04 

82.47 

9.40 

82.42 

9.76 

83 

84 

83.54 

8,78 

83.50 

9.14 

83.46 

9.51 

83,42 

9.87 

84 

85 

84.53 

8.88 

84.50 

9.25 

84.45 

9.62 

84.41 

9.99 

85 

86 

85.53 

8.99 

85.49 

9.36 

85.45 

9.74 

85.40 

10.11 

86 

87 

86.52 

9.09 

86.48 

9.47 

86.44 

9.85 

86.40 

10.23 

87 

88 

87.52 

9.20 

87.48 

9.58 

87.43 

9.96 

87.39 

10.34 

88 

89 

88,51 

9.30 

88.47 

9.69 

88.43 

10.08 

88.38 

10.46 

89 

90 

89.51 

9.41 

89.47 

9.80 

89.42 

10.19 

89.38 

10.58 

90 

91 

90.50 

9.51  1 

90.46 

9.91 

90.42 

10.30 

90.37 

10.70 

91 

92 

91.50 

9.62 

91.45 

10.02 

91.41 

10.41 

91.36 

10.81 

92 

93 

92.49 

9.72 

92.45 

10.12 

92.40 

10.53 

92.36 

10.93 

93 

94 

93.49 

9.83 

93.44 

10.23 

93.40 

10.64 

93.35 

11.05 

94 

95 

94.48 

9.93 

94.44 

10.34 

94.39 

10.75 

94.34 

11.17 

95 

96 

95.47 

10.03 

95.43 

10.45 

95.38 

10.87 

95.33 

11.28 

96 

97 

96.47 

10.14 

96.42 

10.56 

96.38 

10.98 

96.33 

11.40 

97 

98 

97.46 

10.24 

97.42 

10.67 

97.3V 

11.09 

97.32 

11.52 

98 

99 

98.46 

10.35 

98.41 

10.78 

98.36 

11.21 

98.31 

11.64 

99 

100 

99.45 

10.45 

99.41 

10.89 

99.36 

11.32 

99.31 

11.75 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

83 

3 

84  Deg. 

83|  Deg. 

g* 

834  Deg. 

1 

TRAVERSE    TABLE- 


o 

£' 

7  Deg. 

74  Deg. 

71  Deg. 

71  Deg. 

C 

1- 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I 

1 

0.99 

0.12 

0.99 

0.13 

0.99 

0.13 

0.99 

0..13 

1 

2 

1,99 

0,24 

1,98 

0.25 

1.98 

0.26 

1.98 

0.27 

2 

3 

2.98 

0.37 

2,98 

0.38 

2,97 

0.39 

2.97 

0,40 

3 

4 

3.97 

0.49 

3,97 

0.50 

3.97 

0.52 

3.96 

0.54 

4 

5 

4.96 

0.61 

4.96 

0.63 

4,96 

0.65 

4.95 

0.67 

5 

6 

5.96 

0.73 

5  ,95 

0.76 

5.95 

0.78 

5,95 

0.81 

6 

7 

6.95 

0.85 

6.94 

0.88 

6.94 

0,91 

6.94 

0.94 

7 

8 

7.94 

0.97 

7.94 

1.01 

7.93 

,04 

7.93 

1.08 

8 

9 

8.93 

1.10 

8.93 

1.14 

8.92 

,17 

8.92 

1.21 

9 

10 

9.93 

1.22 

9.92 

1.26 

9,91 

.31 

9.91 

1.35 

10 

11 

10.92 

1,34 

10.91 

1.39 

10.91 

.44 

10.90 

1.48 

11 

12 

11.91 

1.46 

11.90 

1.51 

11.90 

.57 

11.89 

1.62 

12 

13 

12,90 

1,58 

12.90 

1.64 

12.89 

.70 

12.88 

1.75 

13 

14 

13.90 

1.71 

13.89 

1.77 

13.88 

1.83 

13.87 

1,89 

14 

15 

14.89 

1.83 

14.88 

1.89 

14.87 

1.96 

14.86 

2.02 

15 

16 

15.88 

1,95 

15.87 

2.02 

15,86 

2.09 

15.85 

2.16 

16 

17 

16.87 

2,07 

16.86 

2.15 

16.85 

2.22 

16.84 

2.29 

17 

18 

17.87 

2.19 

17.86 

2.27 

17.85 

2.35 

17.84 

2.43 

18 

19 

18,86 

2.32 

18.85 

2.40 

18.84 

2.48 

18.83 

2.56 

19 

20 

19.85 

2.44 

19.84 

2,52 

19.83 

2.61  1 

19.82 

2.70 

20 

21 

20.84 

2,56 

20.83 

2.65 

20.82 

2.74 

20.81 

2.83 

21 

22 

21.84 

2.68 

21.82 

2.78 

21.81 

2.87 

21.80 

2.97 

22 

23 

22.83 

2.80 

22.82 

2.90 

22.80 

3.00 

22..  79 

3.  JO 

23 

24 

23.82 

2.92 

23.81 

3,03 

23,79 

3.13 

23.78 

3.24 

24 

25 

24.81 

3.05 

24.80 

3.15 

24.79 

3.26 

24.77 

3.37 

25 

26 

25.81 

3.17 

25.79 

3.28 

25.78 

3.39 

25.76 

3.51 

26 

27 

26.80 

3.29 

26.78 

3.41 

26.77 

3.52 

26.75 

3.64 

27 

28 

27.79 

3.41 

27.78 

3.53 

27.76 

3.65 

27,74 

3.78 

28 

29 

28.78 

3.53 

28.77 

3.66 

28.75 

3.79 

28.74 

3.91 

29 

30 

29.78 

3.66 

29.76 

3.79 

29.74 

3.92 

29  .73 

4.05 

30 

31 

30.77 

3.78 

30.75 

3.91 

30.73 

4.05 

30.72 

4.18 

31 

32 

31.76 

3.90 

31.74 

4.04 

31.73 

4.18 

31.71 

4.32 

32 

33 

32.75 

4.02 

32.74 

4.16 

32.72 

4.31 

32,70 

4,45 

33 

34 

33.75 

4.14 

33.73 

4.29 

33.71 

4.44 

33,69 

4,58 

34 

35 

34.74 

4.27 

34.72 

4.42 

34.70 

4.57 

34.68 

4.72 

35 

36 

35.73 

4.39 

35.71 

4.54 

35.69 

4,70 

35.67 

4.85 

36 

37 

36.72 

4.51 

36.70 

4.67 

36.68 

4.83 

36.66 

4.99 

37 

38 

37.72 

4.63 

37.70 

4.80 

37.67 

4.96 

37.65 

5.12 

38 

39 

38.71 

4.75 

38.69 

4.92 

38.67 

5.09 

38,64 

5,26 

39 

40 

39.70 

4.87 

39.68 

5.05 

39.66 

5.22 

39,63 

5,39 

40 

41 

40.70 

5.00 

40.67 

5.17 

40.65 

5,35 

40.63 

5.53 

41 

42 

41.69 

5.12 

41.66 

5.30 

41.64 

5.48 

41  ,62 

5.66 

42 

43 

42.68 

5.24 

42.66 

5.43 

42.63 

5.61 

42.61 

5.80 

43 

44 

43.67 

5.36 

43.65 

5.55 

43.62 

5.74 

43.60 

5.93 

44 

45 

44.67 

5.48 

44.64 

5.68 

44.62 

5.87 

44.59 

6.0'   45 

46 

45.66 

5.61 

45.63 

5.81 

45.61 

6.00 

45.58   6.20 

46 

47 

46.65 

5.73 

46.62 

5.93 

46.60 

6.13 

i  46.57 

6.34 

47 

48 

4Y.64 

5.85 

47.62 

6.06 

47,59 

6.27 

47.56 

6.47 

48 

49 

48.63 

5.97 

48.61 

6.18 

48,58 

6,40 

48.55 

6.61 

4c 

50 

49.63 

6.09 

49.60 

6.31 

49,57 

6.53 

49.54 

6.74 

50 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

c 
3 

C 

a 

s 

83  Deg. 

82|  Deg. 

82|  Deg. 

824  Deg. 

£ 

TRAVERSE    TABLE. 


17 


o 

OB* 

7  Deg. 

7i  Deg. 

H  Deg. 

7|  Deg. 

a 

F 

,£• 

D 
o 

CO 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

'5 
8 

51 

50.62 

6.22 

50.59 

6.44 

50.56 

6.66 

50.53 

6.88 

51 

52 

51.61 

6.34 

51.58 

6.56 

51.56 

6.79 

51.53 

7.01 

52 

53 

52.60 

6.46 

52.58 

6.69 

52.55 

6.92 

52.52 

7.15 

53 

54 

53.60 

6.58 

53,57 

6.81 

53.54 

7.05 

53.51 

7.28 

54 

55 

54.59 

6.70 

54.56 

6.94 

54.53 

7.18 

54.50 

7.42 

55 

56 

55.58 

6.82 

55.55 

7.07 

55.52 

7.31 

55.49 

7.55 

56 

57 

56.58 

6.95 

56.54 

7.19 

56.51 

7.44 

56.48 

7.69 

57 

58 

57.57 

7.07 

57.54 

7.32 

57.50 

7.57 

57.47 

7.82 

58 

59    58.56 

7.19 

58.53 

7.45 

58.50 

7.70 

58.46 

7.96 

59 

60 

59.55 

7,31 

59.52 

7.57 

59.49 

7.83 

59.45 

8.09 

60 

61 

60.55 

7.43 

60.51 

7.70 

60.48 

7.96 

69.44 

8.23 

31 

62 

61.54 

7.56 

61.50 

7.82 

61.47 

8.09 

61.43 

8.36 

62 

63 

62.53 

7.68 

62.50 

7.95 

62.46 

8.22 

62.42 

8.50 

63 

64 

63.52 

7.80 

63.49 

8.  -08 

63.45 

8.35 

63.42 

8,63 

64 

65 

64.52 

7.92 

64.48 

8  ..20 

64.44 

8.48 

64.41 

8.77 

66 

66 

65.51 

8  .,04 

65.47 

8.33 

65.44 

8.61 

65.40 

8.90 

66 

67 

66  50 

8.17 

66  ,46 

8.46 

66.43 

8.75 

66.39 

9.04 

6?7 

68 

67.  .49 

8.29 

67.46 

8.58 

67.42 

8.88 

67.38 

9.17 

68 

69 

68.49 

8.41 

68.45 

8.71 

68.41 

9.01 

68.37 

9.30 

69 

70 

69  .48 

8.53 

69.44 

8.83 

69.40 

9.14 

69.36 

9.44 

70 

71 

70.47 

8.65 

70.43 

8.96 

70.  30 

9.27 

70.35 

9.57 

71 

72 

71.46 

8.77 

71.42 

9.09 

71.38 

9.40 

71.34 

9.71 

72 

73 

72.46 

8.90 

72.42 

9.21 

72  38 

9.53 

72.33 

9.84 

73 

74 

73.45 

9.02 

73.41 

9.34 

73.37 

9.66 

73.32 

9.98 

74 

75 

74.44 

9.14 

74.40 

9.46 

74.36 

9.79 

74.31 

10.11 

75 

76 

75.43 

9.26 

75.39 

9.59 

75.35 

9.92 

75.31 

10.25 

76 

77 

76.43 

9.38 

76.38 

9.  -72 

76.34 

10.05 

76.30 

10.38 

77 

78 

77.42 

9.51 

77.38 

9.84 

77.33 

10.18 

77.29 

10.52 

78 

79 

78.41 

9.63 

78.37 

9.97 

78.32 

10.31 

78.28 

10.65 

79 

80 

79.40 

9.75 

79.36 

10.10 

79.32 

10.44 

79.27 

10.79 

80 

81 

80.40 

9.87 

80.35 

10.22 

80.31 

10.57 

80.26 

10.92 

81 

82 

81.39 

9.99 

81.34 

10.35 

81.30 

10.70 

81.25 

11.06 

82 

83 

82.38 

10.12 

82.34 

10.47 

82.29 

10.83 

82.24 

11.19 

83 

84 

83.37 

10.24 

83.33 

10.60 

83.28 

10.96 

83.23 

11.33 

84 

85 

84.37 

10.36 

84.32 

10.73 

84.27 

11.09 

84.22 

11.46 

85 

86 

85.36 

10.48 

85.31 

10.85 

85.26 

11.23 

85.21 

11.60 

86 

87 

86.35 

10.60 

86.30 

10.98 

86.26 

11.36 

86.21 

11.73 

87 

88 

87.34 

10.72 

87.30 

11.11 

87.25 

11.49 

87.20 

11.87 

88 

89 

88.34 

10.85 

88.29 

11.23 

88  .24 

11.62 

88.19 

12.00 

89 

90 

89.33 

10  97 

89.28 

11.36 

89.23 

11.75 

89.18 

12.14 

90 

91 

90.32 

11.09 

90.27 

11.48 

90.22 

11.88 

90.17 

12.27 

91 

92 

91.31 

11.21 

91.26 

11.61 

91.21 

12.0-1 

91.16 

12.41 

92 

93 

92.31 

11.33 

92.26 

11.74 

92.20 

12.14 

92.15 

12.54 

93 

94 

93.30 

11.46 

93.25 

11.86 

93.20 

12.27 

93.14 

12.68 

94. 

95 

94.29 

11.58 

94.24 

11.99 

94  ..19 

12.40 

94.13 

12.81 

95 

96 

95,28 

11.70 

95.23 

12.  12 

95.18 

12.53 

95.12 

12.95 

96 

97 

96.28 

11.82 

96.22 

12.24 

96.17 

12.66 

96.11 

13.08 

97 

98 

97.27 

11.94 

97.22 

12.37 

97.16 

12.79 

97.10 

13.22 

98 

99 

98.26 

12.07 

98.21 

12.49 

98.15 

12.92 

98.10 

13.35 

99 

100 

99.25 

12.19 

99.20 

12.62 

99.14 

13.05 

99.09 

13.49 

100 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

p 

6 

I 

1 

Q 

83  Deg. 

82|  Deg. 

82f  Deg. 

82J  Deg. 

3 

TRAVERSE   TABLE. 


g 

8  Deg. 

8*  Deg. 

8£  Deg. 

8i  Deg. 

g 

•   o" 

1" 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

1 

0.99 

0.14 

0.99 

0.14 

0.99 

0.15 

0.99 

0.15 

i 

2 

1.98 

0.28 

1.98 

0.29 

1.98 

0.30 

1.98 

0.30 

2 

3 

2.97 

0.42 

2.97 

0.43 

2.97 

0.44 

2.97 

0.46 

3 

4 

3.  96 

0.56 

3.96 

0.57 

3.96 

0.59 

3.95 

0.61 

4 

5 

4.95 

0.70 

4.95 

0.72 

4.95 

0.74 

4.94 

0.76 

5 

6 

5.94 

0.84 

5.94 

0.86 

5.93 

0.89 

5.93 

0.91 

6 

7 

6.93 

0.97 

6.93 

1.00 

6.92 

.03 

6.92 

1.06 

7 

8 

7.92 

1.11 

7.92 

1.15 

7.91 

.18 

7.91 

1.22 

8 

9 

8.91 

1.25 

8.91 

1  .  29' 

8.90 

.33 

8.90 

1.37 

9 

10 

9.90 

.39 

9.90 

1.43 

9.89 

.48 

9.88 

1.52 

10 

11 

10.89 

.53 

10.89 

1.58 

10.88 

.63 

10.87 

1.67 

11 

12 

11.88 

.67 

11.88 

1.72 

11.87 

.77 

11.86 

1.83 

12 

13 

12.87 

1.81 

12.87 

1  .  87 

12.86 

1.92 

12.85 

1.98 

.13 

14 

13.86 

1.95 

13.86 

2.01 

13.85 

2.07 

13.84 

2.13 

14 

15 

14.85 

2.09 

14.85 

2-15 

14.84 

2.22 

14.83 

2.28 

15 

16 

15.84 

2.23 

15.84 

2.30 

15.82 

2.36 

15.81 

2.43 

16 

17 

16.83 

2.37 

16.83 

2.44 

16.81 

2.51 

16.80 

2.59 

17 

IS 

17.82 

2.51 

17.81 

2.58 

17.80 

2.66 

17.79 

2.74 

18 

19 

18.82 

2.64 

18.80 

2.73 

18.7? 

2.81 

18,78 

2.89 

19 

20 

19.81 

2.78 

19.79 

2.87 

19.78 

2.96 

19.77 

3.04 

20 

21 

20.80 

2.92 

20.78 

3.01 

20  .  77 

3.10 

20.76 

3.19 

21 

22 

21.79 

3.06 

21.77 

3.16 

21.76 

3.25 

21.74 

3  .  35 

22 

23 

22.78 

3.20 

22.76 

3.30 

22  .  75 

3.40 

22.73 

3.50 

23 

24 

23.77 

3.34 

23.75 

3.44 

23.74 

3.55 

23.72 

3.65 

24 

25 

24.76 

3.48 

24.74 

3.59 

24.73 

3.70 

24.71 

3.80 

25 

26 

25  .  75 

3.62 

25.73 

3.73 

25.71 

3.84 

25  .  70 

3.96 

26 

27 

26.74 

3.76 

26.72 

3.87 

26.70 

3.99 

26.69 

4.11 

27 

28 

27.73 

3.90 

27.71 

4.02 

27.69 

4.14 

27.67 

4.26 

28 

29 

28  .  72 

4.04 

28.70 

4.16 

28  .  68 

4.29 

28.66 

4.41- 

29 

30 

29.71 

4.18 

29.69 

4.30 

29.67 

4.43 

29  .  65 

4.56 

30 

31 

30.70 

4.31 

30.68 

4.45 

30.66 

4.58 

30.64 

4.72 

31 

32 

31.69 

4.45 

31.67 

4.59 

31.65 

4.73 

31.63 

4.87 

32 

33 

32.68 

4.59 

32  .  66 

4.74 

32  .  64 

4.88 

32  .  62 

5.02 

33 

34 

33.67 

4.73 

33.65 

4.88 

33.63 

5.03 

33.60 

5.17 

34 

35 

34.66 

4.87 

34.64 

5.02 

34.62 

5.17 

34.59 

5.32 

35 

36 

35.65 

5.01 

35.63 

5.17 

35.60 

5.32 

3.5  .  58 

5.48 

36 

37 

36  .  64 

5  .  15 

36.62 

5.31 

36.59 

5.47 

36.57 

5.63 

37 

38 

37.63 

5.29 

37.61 

5.45 

37  .  58 

5.62 

37.56 

5.78 

38 

39 

38.62 

5.43 

38.60 

5.60 

38  .  57 

5.76 

38.55 

5.93 

39 

40 

39.61 

5.57 

39.59 

5.74 

39.56 

5.91 

39  .  53 

6.08 

40 

41 

40.60 

5.71 

40.58 

5.88 

40.55 

6.06 

40.52 

6.24 

41 

42 

41.59 

5.85 

41.57 

6.03 

41.54 

6.21 

41.51 

6.39 

42 

43 

42.58 

5.98 

42.56 

6.17 

42.53 

6.36 

42.50 

6.54 

43 

44 

43.57 

6.12 

43.54 

6.31 

43  .  52 

6.50 

43.49 

'  6.69 

44 

45 

44.56 

6.26 

44.53 

6.46 

44.51 

6.65 

44.48 

6.85 

45 

46 

45.55 

6.40 

45.52 

6.60 

45.49 

6.80 

45.46 

7.00 

46 

47 

46.54 

6.54 

46.51 

6.74 

46.48 

6.95 

46.45 

7.15 

47 

48 

47.53 

6.68 

47.50 

6.89 

47.47 

7.09 

47.44 

7.30 

48 

49 

48.52 

6.82 

48.49 

7.03 

48.46 

7.24 

48.43 

7.45 

49 

50 

49.51 

6.96 

49.48 

7.17 

49.45 

7.39 

49.42 

7.61 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep- 

Lat. 

1 

3 

•+J 

1 

82  Deg. 

81|  Deg. 

8UDeg. 

81t  Deg. 

M 

P 

TKAVERSE   TABLE. 


c 

8  Deg. 

84  Deg. 

»i  Deg. 

fc}  Deg. 

b 

5' 

p 

P 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

51 

50.50 

7.10 

5fr.47 

7.32 

50.44 

7.54 

50.41 

7.76 

51 

52 

51.49 

7.24 

51.46 

7.46 

51.43 

7.69 

51.39 

7.91 

52 

53 

52.48 

7.38 

52.45 

7.61 

52.42 

7.83 

52.38 

8.06 

53 

54 

53.47 

7.52 

53.44 

7.75 

53.41 

7.98 

53.37 

8.21 

54 

55 

54.46 

7.65 

54.43 

7.89 

54.40 

8.13 

54.36 

8.37 

55 

56 

55.46 

7.79 

55.42 

8.04 

55.38 

8.28 

55.35 

8.52 

56 

57 

56.45 

7.93 

56.41 

8.18 

56.37 

8.43 

56.34 

8.67 

57 

58 

57.44 

8.07 

57.40 

8.32 

57.36 

8.57 

57.32 

8.82 

58 

59 

58.43 

8.21 

58.39 

8.47 

58.35 

8.72 

58.31 

8.98 

59 

60 

59.42 

8.35 

59.38 

8.61 

59.34 

8.87 

59.30 

9.13 

60 

61 

60.41 

8.49 

60.37 

8.75 

60.33 

9.02 

60.29 

9.28 

61 

62 

61.40 

8.63 

61.36 

8.90 

61.32 

9.16 

61.28 

9.43 

62 

63 

62.39 

8.77 

62.35 

9.04 

62.31 

9.31 

62.27 

9.58 

63 

64 

63.38 

8.91 

63.34 

9.18 

63.30 

9.46 

63.26 

9.74 

64 

65 

64.37 

9.05 

64.33 

9.33 

64.29 

9.61 

64.24 

9.89 

65 

66 

65.36 

9.19 

65.32 

9.47 

65.28 

9.76 

65.23 

10.04 

66 

67 

66.35 

9.32 

66.31 

9.61 

66.26 

9.90 

66.22 

10.19 

67 

68 

67.34 

9.46 

67.30 

9.76 

67.25 

10.05 

67.21 

10.34 

68 

69 

68.33 

9.60 

68.29 

9.90 

68.24 

10.20 

68.20 

10.50 

69 

70 

69.32 

9.74 

69.28 

10.04 

69.23 

10.35 

69.19 

10-.65J    70 

71 

70.31 

9.88 

70.27 

10.19 

70.22 

10.49 

70.17 

10.80 

71 

72 

71.30 

10.02 

71.25 

10.33 

71.21 

10.64 

71.16 

10.95 

72 

73 

72.29 

10.16 

72.24 

10.47 

72.20 

10.79 

72.15 

11.10 

73 

74 

73.28 

10.30 

73.23 

10.62 

73.19 

10.94 

73.14 

11.26 

74 

75 

74.27 

10.44 

74.22 

10.76 

74.18 

11.09 

74.13 

11.41 

75 

78 

75.26 

10.58 

75.21 

10.91 

75.17 

11.23 

75.12 

11.56 

76 

77 

76.25 

10.72 

76.20 

11.05 

76.15 

11.38 

76.10 

11.71 

77 

78 

77.24 

10.86 

77.19 

11.19 

77.14 

11.53 

77.09 

11.87 

78 

79 

78,23 

10.99 

78.18 

11.34 

78.13 

11.68 

78.08 

12.02 

79 

80 

79.22 

11.13 

79.17 

11.48 

79.12 

11.82 

79.07 

12.17 

80 

81 

80.21 

11.27 

80.16 

11.62 

80.11 

11.97 

80.06 

12.32" 

81 

82 

81.20 

11.41 

81.15 

11.77 

81.10 

12.12 

81.05 

12.47 

82 

83 

82.19 

11.55 

82.14 

11.91 

82.09 

12.27 

82.03 

12.63 

83 

84 

83.18 

11.69 

83.13 

12.05 

83.08 

12.42 

83.02 

12.78 

84 

85 

84.17 

11.83 

84.12 

12.20 

84.07 

12.56 

84.01 

12.93 

85 

86 

85.16 

11.97 

85.11 

12.34 

85.06 

12.71 

85.00 

13.08 

86 

87 

86.15 

12.11 

86.10 

12.48 

86.04 

12.86 

85.99 

13.23 

87 

88 

87.14 

12.25 

87.09 

12.63 

87.03 

13.01 

86.98 

13.39 

88 

89 

88.13 

12.39 

88.08 

12.77 

88.02 

13.16 

87.96 

13.54 

89 

90 

89.12 

12.53 

89.07 

12.91 

89.01 

13.30 

88.95 

13.69 

90 

31 

90.11 

12.66 

~90706 

13.06 

90.00 

13.45 

89.94 

13.84 

91 

92 

91.10 

12.80 

91.05 

13.20 

90.99 

13.60 

90.93 

14.00 

92 

93 

92.09 

12.94 

92.04 

13.34 

91.98 

13.75 

91.92 

14.15 

93 

94 

93.09 

13.08 

93.03 

13.49 

92.97 

13.89 

92.91 

14.30 

94 

95 

94.08 

13.22 

94.02 

13.63 

93.96 

14.04 

93.89 

14.45 

95 

96 

95.07 

13.36 

95.01 

13.78 

94.95 

14.19 

94.88 

14.60 

96 

97 

96.06 

13.50 

96.00 

13.92 

95.93 

14.34 

95.87 

14.76 

97 

98 

97.05 

13.64 

96.99 

14.06 

96.92 

14.49 

96.86 

14.91 

98 

99 

98.04 

13.78 

97.98 

14.21 

97.91 

14.63 

97.85 

15.06 

99 

100 

99.03 

13.92 

98.97 

14.35 

98.90 

14.78 

98.84 

15.21 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

c3 

."s 
Q 

82  Dog. 

81|  Deg. 

81£  Deg. 

814  Deg. 

1 

TRAVERSE    TABLE. 


o 

9  Deg. 

9$  Deg. 

91  Deg. 

9-!  Deg. 

C 

ES' 

w 

CJ 
(P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

~T 

0.99 

0.16 

0.99 

0.16 

0.99 

0.17 

0.99 

0.17 

1 

2 

1.98 

0.31 

1.97 

0.32 

1.97 

0.33 

1.97 

0.34 

2 

3 

2.96 

0.47 

2.96 

0.48 

2.96 

0.50 

2.96 

0.51 

3 

4 

3.95 

0.63 

3.95 

0.64 

3.95 

0.66 

3.94 

0.68 

4 

5 

4  .  94 

0.78 

4.93 

0.80 

4.93 

0.83 

4.93 

0.85 

5 

6 

5,93 

0.94 

5.92 

0.96 

5.92 

0.99 

5.91 

1.02 

6 

7 

6.91 

1.10 

6.91 

.13 

6.90 

1.16 

6.90 

1.19 

7 

8 

7.90 

1.25 

7.90 

.29 

7.89 

1.32 

7.88 

1.35 

8 

9 

8.89 

1.41 

8.88 

.45 

8.88 

1.49 

8.87 

1.52 

9 

10 

9.88 

1.56 

9.87 

.61 

9.86 

1.65 

9.86 

1.69 

10 

11 

10.86 

1.72 

10.86 

1.77 

10.85 

1.82 

10.84 

1.86 

11 

12 

11.85 

1.88 

11.84 

.93 

11.84 

1.98 

11.83 

2.03 

12 

13 

12.84 

2.03 

12.83 

2.09 

12.82 

2.15 

12.81 

2.20 

13 

14 

13.83 

2.19 

13.82 

2.25 

13.81 

2.31 

13.80 

2.37 

14 

15 

14.82 

2.35 

14.80 

2.41 

14.79 

2.48 

14.78 

2.54 

15 

16 

15.80 

2.50 

15.79 

2.57 

15.78 

2.64 

15.77 

2.71 

16 

17 

16.79 

2.66 

16.78 

2.73 

16.77 

2.81 

1  6  .  75 

2.88 

17 

18 

17.78 

2.82 

17.77 

2.89 

17.75 

2.97 

17.74 

3.05 

18 

19 

18.77 

2.97 

18.75 

3.05 

18.74 

3.14 

IS.  73 

3.22 

19 

20 

19.75 

3.13 

19.74 

3.21 

19.73 

3.30 

19.71 

3.39 

_20 

21 

20.74 

3.29 

20.73 

3.38 

20.71 

3.47 

20.70 

3.56 

21 

22 

21.73 

3.44 

21.71 

3.54 

21.70 

3.63 

21.68 

3.73 

22 

23 

22.72 

3.60 

22.70 

3.70 

22.68 

3.80 

22.67 

3.90 

23 

24 

23.70 

3.75 

23.69 

3.86 

23.67 

3.96 

23.65 

4.06 

24 

25 

24.69 

3.91 

24.67 

4.02 

24.66 

4.13 

24.64 

4.23 

25 

28 

25.68 

4.07 

25.66 

4.18 

25.64 

4.29 

25.62 

4.40 

26 

27 

26.67 

4.22 

26.65 

4.34 

26.63 

4.46 

26.61 

4.57 

27 

28 

27.66 

4.38 

27.64 

4.50 

27.62 

4.62 

27.60 

4.74 

28 

29 

28  .  64 

4.54 

28.62 

4.66 

28.60 

4.79 

28.58 

4.91 

29 

30 

29.63 

4.69 

29.61 

4.82 

29.59 

4.95 

29.57 

5.08 

30 

31 

30.62 

4.85 

30.60 

4.98 

30.57 

5.12 

30.55 

5.25 

31 

32 

31.61 

5.01 

31.58 

5.14 

31.56 

5.28 

31.54 

5.42 

32 

33 

32  .  59 

5.16 

32.57 

5.30 

32.55 

5.45 

32.52 

5.59 

33 

34 

33  .  58 

5.32 

33.56 

5.47 

33.53 

5,61 

33.51 

5.76 

34 

35 

34.57 

5.48 

34.54 

5.63 

34.52 

5.78 

34.49 

5.93 

35 

38 

35.56 

5.63 

35.53 

5.79 

35.51 

5.94 

35.48 

6.10 

36 

37 

36.54 

5.79 

36.52 

5.95 

36.49 

6.11 

36.47 

6.27 

37 

38 

37.53 

5.94 

37.51 

6.11 

37.48 

6.27 

37.45 

6.44 

38 

39 

38  .  52 

6.10 

38.49 

6.27 

38.47 

6.44 

38.44 

6.60 

39 

40 

39.51 

6.26 

39.48 

6.43 

39.45 

6.60 

39.42 

6.77 

40 

11 

40.50 

6.41 

40.47 

6.59 

40.44 

6.77 

40.41 

6.94 

41 

42 

41.48 

6.57 

41.45 

6.75 

41.42 

6.92 

41.39 

7.11 

42 

43 

42.47 

6.73 

42.44 

6.91 

42.41 

7.10 

42.38 

7.28 

43 

44 

43.46 

6.88 

43.43 

7.07 

43.40 

7.26 

43.36 

7,45 

44 

45 

44.45 

7.04 

44.41 

7.23 

44.38 

7.43 

44.35 

7.62 

45 

46 

45.43 

7.20 

45.40 

7.39 

45  .  37 

7.59 

45.34 

7.79 

46 

47 

46.42 

7.35 

46.39 

7.55 

46.36 

7.76 

46.32 

7.96 

47 

48 

47.41 

7.51 

47.38 

7.72 

47.34 

7.92 

47.31 

8.13 

48 

49 

48.40 

7.67 

48.36 

7.88 

48.33 

8.09 

48.29 

8,30 

49 

50 

49  .  38 

7.82 

49.35 

8.04 

49.32 

8.25 

49.28 

8.47 

50 

u 
| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

a 

c 

n 

CO 

"M 

5 

81  Deg. 

80|  Deg. 

801  Deg. 

80i  Deg. 

3 

TKAVEKSE    TABLE, 


21 


d 

55° 

? 

9Deg. 

9*  Deg, 

9^  Deg. 

9.f  Deg. 

g 

1' 

s 
o 

CB 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 
o 

<B 

51 

50.37 

7.98 

50.34 

8.20 

50.30 

8.42 

50.26 

8.64 

~51 

52 

51.36 

8.13 

51.32 

8.36 

51.29 

8.58 

51.25 

8.81 

52 

53 

52.35 

8.29 

52.31 

8.52 

52.27 

8.75 

52.23 

8.98 

53 

54 

53.34 

8.45 

53.30 

8.68 

53.26 

8.91 

53.22 

9.14 

54 

55 

54.32 

8.60 

54.28 

8.84 

54.25 

9.08 

54.21 

9.31 

55 

56 

55.31 

8.76 

55.27 

9.ao 

55.23 

9.24 

55.19 

9.48 

56 

57 

56.30 

8.92 

56.26 

9.16 

56.22 

9.41 

56.18 

9.65 

57 

58 

57.29 

9.07 

57.25 

9.32 

57.20 

9,57 

57.16 

9.82 

58 

59 

58.27 

9.23 

58.23 

9.48 

58.19 

9.74 

58.15 

9.99 

59 

GO 

59.26 

9.39 

59.22 

9.64 

59.18 

9.90 

59.13 

10.16 

60 

61 

60.25 

9.54 

60.21 

9.81 

60.16 

10.07 

60.12 

10.33 

6] 

62 

61.24 

9.70 

61.19 

9.97 

61.15 

10.23 

61.10 

10.50 

62 

63 

62  .  22 

9.86 

62.18 

10.13 

62.14 

10.40 

62.09 

10.67 

63 

64 

63.21 

10.01 

63.17 

10.29 

63.12 

10.56 

63.08 

10.84 

64 

65 

64.20 

10.17 

64.15 

10.45 

64.11 

10.73 

64.06 

11.01 

65 

66 

65.19 

10.32 

65.14 

10.61 

65.09 

10.89 

65.05 

11.18 

66 

67 

66.18 

10.48 

66.13 

10.77 

66.08 

11.06 

66.03 

11.35 

67 

68 

67.16    10.64 

67.12 

10.93 

67.07 

11.22 

67.02 

11.52 

68. 

69 

68.15 

10.79 

68.10 

11.09 

68.05 

11.39 

68.00 

11.69 

69 

70 

69.14 

10.95 

69.09 

11.25' 

69.04 

11.55 

68.99 

11.85 

70 

71 

70.13. 

11.11 

70.08 

11.41 

70.03 

1  1  .  72 

69.97 

12.02 

71 

72 

71.11 

11.26 

71.06 

11.57 

71.01 

11.88 

70.96 

12.19 

72 

73 

72.10 

11.42 

72.05 

11.73 

72.00 

12.05 

71.95 

12.36 

73 

74 

73.09 

11.58 

73.04 

11.89 

72.99 

12.21 

72.93 

12.53 

74 

75 

74.  OS 

1  1  .  73 

74.02 

12.06 

73.97 

12.38 

73.92 

12.70 

75 

70 

75.06 

11.89 

75.01 

12.22 

74.96 

12.54 

74.90 

12.87 

76 

77 

76.05 

12.05 

76.00 

12.38 

75.94 

12.71 

75.89 

13.04 

77 

78 

77.04 

12.20 

76  .  99 

12.54 

76.93 

12.87 

76.87 

13.21 

78 

79 

78,03 

12.36 

77.97 

12.70 

77.92 

13.04 

77.86 

13.38 

79 

80 

79.02 

12.51 

78  .  96 

12.86 

78.90 

13.20 

78.84 

13.55 

80 

81    80.00 

12.67 

79  .  95 

13.02" 

79.89 

13.37 

79.83 

13.72 

81 

82  I  80  .  99 

12.83 

80.93 

13.18 

80.88 

13.53 

80.82 

13.89 

82 

83 

81.98 

12,98 

81.92 

13.34 

81.86 

13.70 

81.80 

14.06 

83 

84 

82  .  97 

13.14 

82.91 

13.50 

82.85 

13.86 

82.79 

14.23 

84 

85  183.95 

13.30 

83.89 

13.66 

S3.83 

14.03 

83.77 

14.39 

85 

88 

84.94 

13.45 

84.88 

13.82 

84.82 

14.19 

84.76 

14.56 

86 

87 

85.93 

13.61 

85.87 

13.  9& 

85.81 

14.36 

85  .  74 

14.73 

87 

88  186.92 

13.77 

86.86 

14.15 

86.79 

14.52 

86.73 

14.90 

88 

89 

87.90 

13.92 

87.84 

14.31 

87.78 

14.69 

87.71 

15.07 

89 

90 

88.89 

14.08 

88.83 

14.47 

88.77 

14.85 

88.70 

15.24 

90 

91 

89.88 

14,24 

89.82 

14.63 

89.75 

15.02 

89.69 

15.41 

91 

92 

90.87 

14.39 

90.80 

14.79 

90.74 

15.18 

90.67 

15.58 

92 

93 

91.86 

14.55 

91.79 

14.95 

91.72 

15.35 

91.66 

15.75 

93 

94 

92.84 

14.70 

92.78 

15.11 

92.71 

15.51 

92.64 

15.92 

94 

95 

93.83 

14.86 

93.76 

15.27 

93.70 

15.68 

93.63 

16.09 

95 

96 

94.82 

15.02 

94.75 

15.43 

94.68 

15.84 

94.61 

16.26 

96 

97 

95.81 

15.17 

95  .  74 

15.59 

95.67 

16.01 

95.60 

16.43 

97 

98 

96.79 

15.33 

96.73 

15.75 

96.66 

16.17 

96.58 

16.60 

98 

99 

97.78 

15.49 

97.71 

15.91 

97.64 

16.34 

97.57 

16.77 

99 

100 

98.77 

15.64 

98.70 

16.07 

98.63 

16.50 

98.56 

16.93 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

a 

Q 

81  Deg. 

80|  Deg. 

80£  Deg. 

8<H  Deg. 

rt 

.s 

Q 

TRAVERSE   TABLE. 


H 

e 

£ 

p 

10  Deg. 

10}  Deg. 

J0£  Deg. 

10|  Deg. 

d 
sr 

p 

3 
o 

C8 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.  . 

Dep. 

a  ; 

o 

CD 

1 

0.98 

0.17 

0.98 

0.18 

0.98 

0.18 

0.98 

0.19 

1 

2 

1.97 

0.35 

1.97 

0.36 

1.97 

0.36 

1.96 

0.37 

a 

3 

2.95 

0.52 

2.95 

0.53 

2.95 

0.55 

2.95 

0  56 

3 

4 

3.94 

0.69 

3.94 

0.71 

3.93 

0.73 

3.93 

0.75 

4 

5 

4.92 

0.87 

4.92 

0.89 

4.92 

0.91 

4.91 

0.93 

5 

6 

5.91 

1.04 

5.90 

1.07 

•5.90 

1.09 

5.89 

]  ,12 

6 

7 

6.89 

1.22 

6.89 

1.25 

6.88 

1.28 

6.88 

1.31 

7 

8 

7.88 

1.39 

7.87 

1.42 

7.87 

1.46 

7.86 

1.49 

8 

9 

8.86 

1.56 

8.86 

1.60 

8.85 

1.64 

8.84 

1.68 

9 

10 

9.85 

1.74 

9.84 

1.78 

'9.83 

1.82 

9.82 

1.87 

10 

11 

10.83 

1.91 

10.82 

1.96 

10.82 

2.00 

10.81 

2.05 

11 

12 

11.82 

2.08 

11.81 

2.14 

11.80 

2.19 

11.79 

2.24 

12 

13 

12.80 

2.26 

12.79 

2.31 

12.78 

2.37 

12.77 

2.42 

13 

14 

13.79 

2.43 

13.78 

2.49 

13.77 

2.55 

13.75 

2.61 

14 

15 

14.77 

2.60 

14.76 

2.67 

14.75 

2.73 

14.74 

2.80 

15 

16 

15.76 

2.78 

15.74 

2.85 

15.73 

2.92 

15.72 

2.98 

16 

17 

16.74 

2.95 

16.73 

3.03 

16.72 

3.10 

16.70 

3.J7 

17 

18 

17.73 

3.13 

17.71 

3.20 

17.70 

3.28 

17.68 

3.36 

18 

19 

18.71 

3.30 

18.70 

3.38 

18.68 

3.46 

18.67 

3.54 

19 

20 

19.70 

3.47 

19.68 

3.56 

19.67 

3.64 

19.65 

3.73 

20 

21 

20.68 

3.65 

20.66 

3.74 

20.65 

3.83 

20.63 

3.92 

21 

22 

21.67 

3.82 

21.65 

3.91 

21.63 

4.01 

21.61 

4.10 

22 

23 

22  .  65 

3.99 

22.63 

4.09 

22.61 

4.19 

22.60 

4.29 

23 

24 

23.64 

4.17 

23.62 

4.27 

23.60 

4.37 

23.58 

4.48 

24 

25 

24.62 

4,34 

24.60 

4.45 

24.58 

4.56 

24.56 

4.66 

25 

26 

25.61 

4.51 

25  .  59 

4.63 

25.56 

4.74 

25.54 

4.85 

26 

27 

26.59 

4.69 

26.57 

4.80 

26.55 

4.92 

26.53 

5.04 

27 

28 

27.57 

4.86 

27.55 

4.98 

27.53 

5.10 

27.51 

5.22 

28 

29 

28.56 

5.04 

28.54 

5.16 

28.51 

5.28 

28.49 

5.41 

29 

30 

29.54 

5.21 

29.52 

5.34 

29.50 

5.47 

29.47 

5.60 

30 

31 

30.53 

5.38 

30.51 

5.52  I 

30.48 

5.65 

30.46 

5.78 

31 

32 

31.51 

5,56 

31.49 

5.69 

31.46 

5.83 

31.44 

5.97 

32 

33 

32.50 

5.73 

32.47 

5.87 

32.45 

6.01 

32.42 

6.16 

33 

34 

33.48 

5.90 

33.46- 

6.05 

33.43 

6.20 

33.40 

6.34 

34 

35 

34.47 

6.08 

34.44 

6.23 

34.41 

6.38 

34.39 

6.53 

35 

36 

35.45 

6.25 

35.43 

6.41 

35.40 

6.56 

35.37 

6.71 

3f> 

37 

36.44 

6.42 

36.41 

6.58 

36.38 

6.74 

36.35 

6.90 

37 

38 

37.42 

6.60 

37.39 

6.76 

37.36 

6.92 

37.33 

7.09 

38 

39 

38.41 

6.77 

38.38 

6.94 

38.35 

7.11 

38.32 

7.27 

39 

40 

39.39 

6.95 

39.36 

7.12 

39.33 

7.29 

39.30 

7.46 

40 

41 

40.38 

7.12 

40.35 

7.30 

40.31 

7.47 

40.28 

7.65 

41 

42 

41.36 

7.29 

41.33 

7.47 

41.30 

7.65 

41.26 

7.83 

42 

43 

42.35 

7.47 

42.31 

7.65 

42.28 

7.84 

42.25 

8.02 

•  43 

44 

43.33 

7.64 

43.30 

7.83 

43.26 

8.02 

43.23 

8.21 

44 

45 

44.32 

7.81 

44.28 

8.01 

44.25 

8.20 

44.21 

8.39 

45 

46 

45.30 

7.69 

45.27 

8.19 

45.23 

8.38 

45.19 

8.58 

46 

47 

46.29 

8.16 

46.25 

8.36 

46.21 

8.57 

46.18 

8.77 

47 

48 

47.27 

8.34 

47.23 

8.54 

47.20 

8.75 

47.16 

8.95 

48 

49 

48.26 

8.51 

48.22 

8.72 

48.18 

8.93 

48.14 

9.14 

49 

50 

49.24 

8.68 

49.20 

8.90 

49.16 

9.11 

49.12 

9.33 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

CO 

o 

g 

1 

n 

BO 

Q 

80  Deg. 

79|  Deg. 

79£  Deg. 

791  Deg. 

3 

TKAVEI1SE    TA11LE. 


II 

o 

w' 

10  Deg. 

10J  Deg. 

IQi  Deg. 

10|  Deg. 

0 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 
o 

CD 

5j 

50.23 

8.86 

50.19 

9.08 

50.15 

9.29 

50,10 

9.51 

51 

52 

51.21 

9.03 

51.17 

9.25 

51.13 

9.48 

51.09 

9  .  70 

52 

53 

52.19 

9.20 

52.15 

9.43 

52  .  1  1 

9.66 

52.07 

9.89 

53 

54    53.18 

9.38 

53.14 

9.61 

53.10 

9.84 

53.05 

10.07 

54 

55 

54.16 

9.55 

54.12 

9.79 

54.08 

10.02 

54.03 

10.26 

55 

56 

55.15 

9.72 

55.11 

9.96 

55.06 

10.21 

55.02 

10.45 

56 

57 

56.13 

9.90 

56.09 

10.14 

56.05 

10.39 

56.00 

10.63 

57 

58 

57.12 

10.07 

57.07 

10.32 

57.03 

10.57 

56.98 

10.82 

58 

59 

58,10 

10.25 

58.06 

10.50 

58.01 

10.75 

57.96 

11.00 

59 

60 

59.09 

10.42 

59.04 

10.68 

59.00 

10.93 

58.95 

11.19 

60 

61 

60.07 

10.59 

60.03 

10.85 

59  .98 

11.12 

59.93 

11.38 

61 

62 

61.06 

10.77 

61.01 

11.03 

60.96 

11.30 

60.91 

11.56 

62 

63 

62.04 

10.94 

61.99 

11.21 

61.95 

11.48 

61.89 

11.75 

63 

64 

63.03 

11.11 

62.98 

11.39 

62.93 

11.66 

62.88 

11.94 

64 

65 

64.01 

11.29 

63.96 

1  1  .  57 

63.91 

11.85 

63.86 

12.12 

65 

66 

65.00 

11.46 

64.95 

11.74 

64.89 

12.03 

64.84 

12.31 

66 

67 

65.98 

11.63 

65.93 

11.92 

65.88 

12.21 

65.82 

12.50 

67 

68 

66.97 

11.81 

66.91 

12.10 

66.86 

12.39 

66.81 

12.68 

68 

69 

67.95 

11.98 

67.90 

12.28 

67.84 

12.57 

67.79 

12.87 

69 

70 

68.94 

12.  IF 

68.88 

12.46 

68.83 

12.76 

68.77 

13.06 

70 

71 

69.92 

12.33 

69.87 

12.63 

69.81 

12.94 

69.75 

13.24 

7J 

72 

70.91 

12.50 

70.85 

12.81 

70.79 

13.12 

70.74 

13.43 

72 

73 

71.89 

12.68 

71.83 

12.99 

71.78 

13.30 

71.72 

13.62 

73 

74 

72.88 

12.85 

72.82 

13.17 

72  .  76 

13.49 

72.70 

13.80 

74 

75 

73.86 

13.02 

73.80 

13.35 

73.74 

13.67 

73.68 

13.99 

75 

76 

74.85 

13.20 

74.79 

13.52 

74.73 

13.85 

74.67 

14.18 

76 

77 

75.83 

13.37 

75  .  77 

13.70 

75.71 

14.03 

75.65 

14.36 

77 

78 

76.82 

13.54 

76.76 

13.88 

76.69 

14.21 

76  .  63 

14.55 

78 

79 

77.80 

13.72 

77.74 

14.06 

77.68 

14.40 

77.61 

14.74 

79 

80 

78  .  78 

13.89 

78.72 

14.24 

78.66 

14.58 

78.60 

14.92 

80 

81 

79.77 

14.07 

79.71 

14.41 

79  .  64 

14.76 

79.58 

15.  if 

81 

82 

80.75 

14.24 

80.69 

14.59 

80.63 

14.94 

80.56 

15.29 

82 

83 

81.74 

14.41 

81.68 

14.77 

81.61 

15.13 

81.54 

15.48 

83 

84 

82.72 

14.59 

82.66 

14.95 

82.59 

15.31 

82.53 

15.67 

84 

85 

83.71 

14.76 

83  .  64 

15.13 

83.58 

15.49 

83.51 

15.85 

85 

86 

84.69 

14.93 

84.63 

15.30 

84.56 

15.67 

84.49 

16.04 

86 

87 

85.68 

15.11 

85.61 

15.48 

85.54 

15.85 

85.47 

16.23 

87 

88 

86.66 

15.28 

86.60 

15.66 

86.53 

16.04 

83.46 

16.41 

88 

89 

87.65 

15.45 

87.58 

15.84 

87.51 

16.22 

87.44 

16.60 

89 

90 

88.63 

15.63 

88.56 

16.01 

88.49 

16.40 

88.42 

16.79 

90 

91 

89.62 

15.80 

89.55 

16.19 

89.48 

16.53 

89.40 

16.97      91 

92 

90.60 

15.98 

90.53 

16.37 

90.46 

16.77 

90.39 

17.16      92 

93 

91.59 

16.15 

91.52 

16.55 

91.44 

16.95 

91.37 

17.35 

93 

94 

92.57 

16.32 

92.50 

16.73 

92.43 

17.13 

92.35 

17.53 

94 

95 

93  .  56 

16.50 

93.48 

16.90 

93.41 

17.31 

93.33 

17.72 

95 

96 

94.54 

16.67 

94.47 

17.08 

94.39 

17.49 

94.32 

17.91 

96 

97 

95.53 

16.84 

95.45 

17.26 

95.38 

17.68 

95.30 

18.09 

97 

98 

96.51 

17.02 

96.44 

17.44 

96.36 

17.86 

96.28 

18.28 

98 

99 

97.50 

17.19 

97.42 

17.62 

97.34 

18.04 

97.26 

18.47 

99 

100 

98.48 

17.36 

98.40 

17.79 

98.33 

18.22 

98.25 

18.65 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

ci 

•I 

80  Deg. 

79|  Deg. 

79£  Deg. 

794  Deg. 

oj 

CO 

Q 

24 


TRAVJiKSE    TABLE. 


I 

11  Deg. 

1H  Deg. 

11$  Deg. 

11|  Deg. 

P 

s 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

t3 

P 

1 

0.98 

0.19 

0.98 

0.20 

0.98 

0.20  1 

0.98 

0.20 

r 

2 

1.96 

0.38 

1.96 

0.39 

1.96 

0.40 

1.96 

0.41 

2 

3 

2.94 

0.57 

2.94 

0.59 

2.94 

0.60 

2.94 

0.61 

3 

4 

3.93 

0.76 

3.92 

0.78 

3.92 

0.80 

3.92 

0.82 

4 

5 

4.91 

0.95 

4.90 

0.98 

4.90 

1.00 

4.90 

1.02 

5 

6 

5.89 

1.14 

5.88 

1.17 

5.88 

1.20 

5.87 

1.22 

6 

7 

6.87 

1.34 

6.87 

1.37 

6.86 

1.40 

6.85 

1.43 

7 

8 

7.85 

1.53 

7.85 

1.56 

7.84 

1.59 

7.83 

1.63 

8 

9 

8.83 

1.72 

8.83 

1.76 

8.82 

1.79 

8.81 

1.83 

9 

10 

9.82 

1.91 

9.81 

1.95 

9.80 

1.99 

9.79|  2.04 

10 

11 

10.80 

2.10 

10.79 

2.15 

10.78 

2.19  i 

10.77 

2.24 

11 

12 

11.78 

2.29 

11.77 

2.34 

11.76 

2.39 

11.75 

2.44 

12 

13 

12.76 

2.48 

12.75 

2.54 

12.74 

2.59 

12.73 

2.65 

13 

14 

13.74 

2.67 

13.73 

2.73 

13.72 

2.79 

13.71 

2.85 

14 

15 

14.72 

2.86 

14.71 

2.93 

14.70 

2.99 

14.69 

3.06 

'  15 

16 

15.71 

3.05 

15.69 

3.12 

15.68 

3.19 

15.66 

3.26 

16 

17 

16.69 

3.24 

16.67 

3.32 

16.66 

3.39 

16.64 

3.46 

17 

18 

17.67 

3.43 

17.65 

3.51 

17.64 

3.59 

17.62 

3.66 

18 

19 

18.65 

3.63 

18.63 

3.71 

18.62 

3.79 

18.60 

3.87 

19 

20 

19.63 

3.82 

19.62 

3.90 

19.60 

3.99 

19.58 

4.07 

20 

21 

20.61 

4.01 

20  .  60 

4.10 

20  .  58 

4.19 

20  .  56 

4.28 

21 

22 

21.60 

4.20 

21.58 

4.29 

21.56 

4.39 

21.54 

4.48 

22 

23 

22.58 

4.39 

22.56 

4.49 

22.54 

4.59 

22.52 

4.68 

23 

24 

23.56 

4.58 

23.54 

4.68 

23  .  52 

4.78 

23.50 

4.89 

24 

25 

24.54 

4.77 

24.52 

4.88 

24.50 

4.98 

24.48 

5.09 

25 

26 

25.52 

4.96 

25  .  50 

5.07 

25.48 

5.18 

25.46 

5.30 

26 

27 

26.50 

5.15 

26.48 

5.27 

26.46 

5.38 

26.43 

5  .  50 

27 

28 

27.49 

5.34 

27.46 

5.46 

27.44 

5.58 

27.41 

5  .  70 

28 

29 

28.47 

5.53 

28.44 

5.66 

28.42 

5.78 

28.39 

5.91 

29 

30 

29.45 

5.72 

29.42 

5.85 

29.40 

5.98 

29.37 

6.11 

30 

31 

30.43 

5.92 

30.40 

6.05 

30.38 

6.18 

30.35 

6.31 

8.1 

32 

31.41 

6.11 

31.39 

6.24 

31.36 

6.33 

31.33 

6  .  52 

32 

33 

32.39 

6-30 

32.37 

6.44 

32.34 

6.58 

32.31 

6.72 

33 

34 

33.38 

6.49 

33.35 

6.63 

33.32 

6.78 

33.29 

6.92 

34 

35 

34.36 

6.68 

34.33 

6.83 

34.30 

6  .  93 

34.27 

7.13 

35 

36 

35.34 

6.87 

35.31 

7.02 

35.28 

7.18 

35  .  25 

7.33 

36 

37 

36.32 

7.06 

36.29 

7.22 

36.26 

7.38 

36.22 

7.53 

37 

38 

37.30 

7.25 

37.27 

.7.41 

37.24 

7.58 

37.20 

7.74 

38 

39 

38.28 

7.44 

38.25 

7.61 

38.22 

7.78 

38.18 

7.94 

39 

40 

39.27 

7.63 

39.23 

7.80 

39.20 

7.97 

39.18 

8,15 

40 

41 

40.25 

7.82 

40.21 

8.00 

40.18 

8.17 

40  .  14 

8.35 

41 

42 

41.23 

8.01 

41.19 

8.19 

41.16 

8.37 

41.12 

8.55 

42 

43 

42.21 

8.20 

42.17 

8.39 

42.14 

8.5? 

42.10 

8.76 

43 

44 

43.19 

8.40 

43.15 

8  .  58 

43.12 

8.77 

43.08 

8.96 

44 

45 

44.17 

8.59 

44.14 

8.78 

44.10 

8.97 

44.06 

9.16 

45 

46 

45.15 

8.78 

45.12 

8.97 

45  .  08 

9.17 

45.04 

9.37 

46 

4? 

46.14 

8.97 

46.10 

9.17 

46.06 

9.37 

48.02 

9.57 

47 

48 

47.12 

9.16 

47.08 

9.36 

47.04   9.57 

46.99 

.9.78 

48 

49 

48.10 

9.35 

48.06J  9.56 

48.02   9.77 

47.97 

9.98 

49 

50 

49.08 

9.54 

49.04J  9.75 

49.00)  9.97 

48.95 

10.18 

50 

8 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

to 

o 
C 

4 

"^ 

P 

79  Deg. 

78!  Deg. 

18$  Deg. 

78J  Deg. 

Q 

TRAVERSE    TABLE. 


25 


(3 

11  Deg. 

Hi  Deg. 

11*  Deg. 

Ill  Deg, 

O 

p 

P?" 

a 
o 

0) 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

§ 

TT 

50.06 

9.73 

50  .  02 

9.95 

49.98 

10.17 

49.93 

10.39 

51 

52 

51.04 

9.92 

51.00 

10.14 

50.96 

10.37 

50.91 

10.59 

52 

53 

52.03 

10.11 

51.98 

10.34 

51.94 

10.57 

51.89 

10.79 

53 

54 

53.01 

10.30 

52.96 

10.53 

52.92 

10.77 

52.87 

11.00 

54 

55 

53.99 

10.49 

53.94 

10.73 

53.90 

10.97 

53.85 

11.20 

55 

56 

54.97 

10.69 

54.92 

10.93 

54.88 

11.16 

54.83 

11.40 

56 

57 

55.95 

10.88 

55.90 

If.  12 

55.86 

11.36 

55.81 

11.61 

57 

58 

56.93 

11.07 

56.89 

11.32 

56.84 

11.56 

56.78 

11.81 

58 

59 

57.92 

11.26 

57.87 

11.51 

57.82 

11.76 

57.76 

12.01 

59 

GO 

58.90 

11.45 

58.85 

11.71 

58.80 

11.96 

58.74 

12.22 

60 

61 

59.88 

11.64 

59.83 

11.90 

59.78 

12.16 

59  .  72 

12.42 

61 

62 

60.86 

11.83 

60.81 

12.10 

60.76 

12.36 

60.70 

12.63 

62 

63 

61.84 

12.02 

61.79 

12.29 

61.74 

12.56 

61.68 

12.83 

63 

64 

62.82 

12.21 

62.77 

12.49 

62.72 

12.76 

62.66 

13.03 

64 

65 

63.81 

12.40 

63.75 

12.68 

63.70 

12.96 

63.64 

13.24 

65 

66 

64.79 

12.59 

64.73 

12.88 

64.68 

13.16 

64.62 

13.44 

66 

-    67 

65.77 

12.78 

65.71 

13.07 

65  .  66 

13.36 

65.60 

13.64 

67 

63 

66.75 

12.98 

66.69 

13.27 

66  .  63 

13.56 

66.58 

13.85 

68 

69 

67.73 

13.17 

67.67 

13.46 

67.61 

13.76 

67.55 

14.05 

69 

70 

68.71 

13.36 

68.66 

13.66 

68.59 

13.96 

68.53 

14.25 

70 

;  ~i7 

69.70 

13.55 

69.64 

13.85 

69.57 

14.16 

69.51 

14.46 

71 

72 

70.68 

13.74 

70.62 

14.05 

70.55 

14.35 

70.49 

14.66 

72 

73 

71.66 

13.93 

71.60 

14.24 

71.53 

.'4.55 

71.47 

14.87 

73 

74 

72.64 

14.12 

72.58 

14.44 

72.51 

14.75 

72.45 

15.07 

74 

75 

73  .  62 

14.31 

73.56 

14.63 

73.49 

14.95 

73.43 

15.27 

75 

76 

74.60 

14.50 

74.54 

14.83 

74.47 

15.15 

74.41 

15.48 

76 

77 

75  .  59 

14.69 

75.52 

15.02 

75.45 

15.35 

75.39 

15.68 

77 

?M 

76  .  57 

14.88 

76.50 

15.22 

76.43 

15.55 

76.37 

15.88 

78 

79 

77.55 

15.07 

77.48 

15.41 

77.41 

15.75 

77.34 

16.09 

79 

8!) 

78.53     15.26 

78.46 

15.61 

78.39 

15.95 

78.32 

16.29 

80 

81 

79.51     15.46 

79.44 

15.80 

79.37 

16.15 

79.30 

16.49 

81 

83 

80.49 

15.65 

80.42 

16.00 

80.35 

16.35 

80.28 

16.70 

82 

83 

81.48 

15.84 

81.41 

16.19 

81.33 

16.55 

81.26 

16.90 

83 

84 

82.46 

16.03 

82.39 

16.39 

82.31 

16.75 

82.  -24 

17.11 

84 

85 

33.44 

16.22 

83.37 

16.58 

83.29 

16.95 

83.22 

17.31 

85 

86 

84.42 

16.41 

84  .  35 

16.78 

84.27 

17.15 

84.20 

17.51 

86 

87 

85.40 

16.60 

85  .  33 

16.97 

85.25 

17.35 

85.18 

17.72 

87 

88 

86.38 

16.79 

86.31 

17.17 

86.23 

17.54 

86.16 

17.92 

88 

89    87.33 

16.98 

87.29 

17.36 

87.21 

17.74 

87.14 

18.12 

89 

90    88.35)  17.17 

88.27 

17.56 

88.19 

17.94 

88.11 

18.33 

90 

91 

89.33  |  17.36 

89.25 

17.75 

89".  17 

18.14 

89.09 

18.53 

91 

92 

90.31 

17.55 

90.23 

17.95 

90.15 

18.34 

90.07 

18.74 

92 

93    91.29 

17.75 

91.21 

18.14 

91.13 

18.54 

91.05 

18.94 

93 

94  i  92.27 

17.94 

92.19 

18.34 

92.11 

18.74 

92.03 

19.14 

94 

95193.25 

18.13 

93.17 

18.53 

93.09 

18.94 

93.01 

19.35 

95 

98  |  94.24 

18.32 

94.16 

18,73 

94.07 

19.14 

93  .  99 

19.55 

96 

97  1  95.22 

18.51 

95.14 

18..  92 

95.05 

19.34 

94.97 

19.75 

97 

98 

96.20 

18.70 

96.12 

19.12 

96.03 

19.54 

95.95 

19.96 

98 

99 

97.18 

18.89 

97.10 

19.31 

97.01 

19.74 

96.93 

20.16 

99 

100 

98  .  16 

19.08 

98.08 

19.51 

97.99 

19.94 

97.90 

20.36 

100 

o 
u 
e 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

»" 

o 

S 

S 

79  Deg. 

78|  Deg. 

78$  Deg.    • 

78*  Deg. 

£ 

CO 

Q 

TRAVERSE    TABLE. 


i         1 

s 

B 

12  Deg. 

124  Deg. 

12|  Deg. 

12J  Deg. 

O 

ST 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

1 

0.98 

0.21 

0.98 

0.21 

0.98 

0.22 

0.98 

0.22 

~T 

2 

1.96 

0.42 

1.95 

0.42 

1.95 

0.43 

1.95 

0.44 

2 

3 

2.93 

0.62 

2.93 

0.64 

2.93 

0.65 

2.93 

0.66 

3 

4 

3.91 

0.83 

3.91 

0.85 

3.91 

0.87 

3.90 

0.88 

4 

5 

4.89 

1.04 

4.89 

1.06 

4.88 

1.08 

4.88 

1.10 

5 

6 

5.87 

1.25 

5.86 

1.27 

5.86 

1.30 

5.85 

1.32 

6 

7 

6.85 

1.46 

6.84 

1.49 

6.83 

1.52 

6.83 

1.54 

7 

8 

7.83 

1.66 

7.82 

1.70 

7.81 

1.73 

7.80 

1.77 

8 

9 

8.80 

1.87 

8.80 

1.91 

8.79 

1.95 

8.78 

1.99 

9 

10 

9.78 

2.08 

9.77 

2.12 

9.76 

2.16 

9.75 

2.21 

10 

11 

10.76 

2.29 

10.75 

2.33 

10.74 

2.38 

10.73 

2.43 

11 

12 

11.74 

2.49 

11.73 

2.55 

11.72 

2.60 

11.70 

2.65 

12 

13 

12.72 

2.70 

12.70 

2.76 

12.69 

2.81 

12.68 

2.87 

13 

14 

13.69 

2.91 

13.68 

2.97 

13.67 

3.03 

13.65 

3.09 

14 

15 

14.67 

3.12 

14.66 

3.18 

14.64, 

3.25 

14.63 

3.31 

15 

16 

15.65 

3.33 

15.64 

3.39 

15.62 

3.46 

15.61 

3.53 

16 

17 

16.63 

3.53 

16.61 

3.61 

16.60 

3.68 

16.58 

3.75 

17 

18 

17.61 

3.74 

17.59 

3.82 

17.57 

3.90 

17.  i  r,6 

3.97 

18 

19 

18.58 

3.95 

18.57 

4.03 

18.55 

4.11 

18.53 

4.19 

19 

20 

19.56 

4.16 

19.54 

4.24 

19.53 

4.33 

19.51 

4.41 

20 

21 

20.54 

4.37 

20.52 

4.46 

20  .  50 

4.55 

20.48 

4.63 

21 

22 

21.52 

4.57 

21.50 

4.67 

21.48 

4.76 

21.46 

4.86 

22 

23 

22.50 

4.78 

22.48 

4.88 

22.45 

4.98 

22.43 

5.08 

23 

24 

23.48 

4.99 

23.45 

5.09 

23.43 

5.19 

23.41 

5.30 

24 

25 

24.45 

5.20 

24.43 

5.30 

24.41 

5.41 

24.38 

5.52 

25 

26 

25.43 

5.41 

25.41 

5.52 

25.33 

5.63 

25.36 

5.74 

26 

27 

26.41 

5.61 

26.39 

5.73 

26.36 

5.84 

26.33 

5.96 

27 

28 

27.39 

5.82 

27.36 

5.94 

27.34 

6.06 

27.31 

6.18 

28 

29 

28.37 

6.03 

28.34 

6.15 

28.31 

6.28 

28.28 

6.40 

29 

30 

29.34 

6.24 

29.32 

6.37 

29.29 

6.49 

29.26 

6  .  62 

30 

31 

30.32 

6.45 

30.29 

6.58 

30.27 

6.71 

30.24 

6.84 

31 

32 

31.30 

6.65 

31.27 

6.79 

31.24 

6.93 

31.21 

7.06 

32 

33 

32.28 

6.86 

32.25 

7.00 

32.22 

7.14 

32.19 

7.28 

33 

34 

33.26 

7.07 

33.23 

7.21 

33.19 

7.36 

33.16 

7.50 

34 

35 

34.24 

7.28 

34.20 

7.43 

34.17 

7.58 

34.14 

7.72 

35 

36 

35.21 

7.48 

35.18 

7.64 

35.15 

7.79 

35  .  1  1 

7.95 

36 

37 

36.19 

7.69 

36.16 

7.85 

36.12 

8.01 

36.09 

8.17 

37 

38 

37.17 

7.90 

37.13 

8.06 

37.10 

8.22 

37.06 

8.39 

38 

39 

38.15 

8.11 

38.11 

8.27 

38.08 

8.44 

38.04 

8.61 

39 

40 

39.13 

8.32 

39.09 

8.49 

39.05 

8.66 

39.01 

8.83 

40 

41 

40.10 

8.52 

40.07 

8.70 

40.03 

8.87 

39.99 

9.05 

41 

42 

41.08 

8.73 

41.04 

8.91 

41.00 

9.09 

40.96 

9.27 

42 

43 

42.06 

8.94 

4?.  02 

9.12 

41.98 

9.31 

41.94 

9.49 

43 

44 

43.04 

9.15 

43.00 

9.34 

42.96 

9.52 

42.92 

9.71 

44 

45 

44.02 

9.36 

43.98 

9.55 

43.93 

9.74 

43.89 

9.93 

45 

46 

44.99 

9.56 

44.95 

9.76 

44.91 

9.96 

44.87 

10.15 

46 

47 

45.97 

9.77 

45.93 

9.97 

45.89 

10.17 

45.84 

10.37 

47 

48 

46.95 

9.98 

46.91 

10.18 

46.86 

10.39 

46.82 

10.59 

48 

49 

47.93 

10.19 

47.88 

10.40 

47.84 

10.61 

47.79 

10.81 

49 

50 

48.91 

10.40 

48.86 

10.61 

48.81 

10.82 

48.77 

11.03 

50 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 
o 

a 

1 

78  Deg. 

77|  Deg. 

77^  Deg. 

774  Deg. 

Q 

TRAVERSE    TABLE. 


27 


5 

55 

12  Deg. 

12}  Deg. 

12£  Deg. 

12|  Deg. 

O 

tance. 

1' 

o 

cu 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

49.89 

10.00 

49.84 

10.82 

49.79 

11.04 

49  .  74 

11.26 

51 

52 

50.86 

10.81 

50,82 

11.03 

50.77 

11,25 

50.72 

11.48 

52 

53 

51.84 

11.02 

51.79 

11.25 

51.74 

11.47 

51.69 

11.70 

53 

54 

52.82 

11,23 

52.77 

11.46 

52.72 

11.69 

52.67 

11.92 

54 

55 

53.80 

11.44 

53..  75 

'1.67 

53.70 

11.90 

53.64 

12.14 

55 

58 

54.78 

11,64 

54.72 

11.88 

54.67 

12,12 

54,62 

12.36 

56 

57 

55.75 

11.85 

55  .  70 

12.09 

55.65 

12.34 

55  .  59 

12.58 

57 

58 

56.73 

12.06 

56  .  68 

12.31 

56  .  63 

12.55 

56  .  57 

12.80 

58 

59 

57.71 

12.27 

57.66 

12.52 

57.60 

12.77 

57.55 

13.02 

59 

60 

58.69 

12.47 

58.63 

12.73 

58,58 

12.99 

58,52 

13.24 

60 

61 

59.67 

12.68 

59.61 

12,94 

59  .  55 

13.20 

59.50 

13.46 

01 

62 

60,65 

12.89 

60.59 

13.16 

60.53 

13.42 

60.47 

13.68 

62 

63 

61.62 

13.10 

61.57 

13.37 

61.51 

13.64 

61.45 

13.90 

63 

64 

62  .  60 

13.31 

62.54 

13.58 

62,48 

13.85 

62.42 

14.12 

64 

65 

63.58 

13.51 

63.52 

13.79 

163.46 

14.07 

63.40 

14.35 

65 

66 

64.56 

13.72 

64.50 

14.00 

64,44 

14.29 

64.37 

14.57 

06 

67 

65.54 

13.93 

65.47 

14.22 

65.41 

14.50 

65.35 

14.79 

67 

68 

66.51 

14.14 

66.45 

14.43 

66.39 

14.72 

66.32 

15.01 

68 

69 

67.49 

14.35 

67.43 

14.64 

67.36 

14.93 

67.30 

15.23 

69 

70 

68.47 

14.55 

68.41 

14.85 

68.34 

15.15 

68.27 

15.45 

70 

71 

69.45 

14.76 

69.38 

15.06 

69.32 

15.37 

69  .  25 

15.67" 

71 

72 

70.43 

14.97 

70.36 

15.28 

70.29 

15.58 

70.22 

15.89 

72 

73 

71.40 

15.18 

71.34 

15.49 

71.27 

15.80 

71.20 

16   11      73 

74 

72.38 

15.39 

72.32 

35.70 

72.25 

16.02 

72.18 

16.33 

74 

75 

73.36 

15.59 

73.29 

15.91 

73.22 

16.23 

73.15 

16.55 

75 

76 

74.34 

15.80 

74.27 

16.13 

74.20 

16.45 

74.13 

16.77 

76 

77 

75  .  32 

16.01 

75.25 

16.34 

75.17 

16.67 

75.10 

16.99 

77 

78 

76.30 

16  .  22 

76.22 

16.55 

76.15 

16.88 

76.08 

17.21 

78 

79 

77.27 

16.43 

77.20 

16.76 

77.13 

17.10 

77.05 

17.44 

79 

80 

78.25 

16.63 

78.18 

16.97 

78.10 

17.32 

78.03 

17.66 

80 

81 

79.23 

16.84 

79.16 

17.19 

79.08 

17.53 

79.00 

17.88 

81 

Of> 

80.21 

17.05 

80.13 

17.40 

80.06 

17.75 

79.98 

18.10 

82 

83 

81.19 

17.26 

81.11 

17.61 

81.03 

17.96 

80.95 

18.32 

83 

84 

82.16 

17.46 

82.09 

17.82 

82.01 

18.18 

81.93 

18.54 

84 

85 

83.14 

17.67 

83.06 

18.04 

82  .  99 

18.40 

82.90 

18.76 

85 

86 

84.12 

17.88 

84.04 

18.25 

83.96 

18.61 

83.83 

18.98 

86 

87 

85.10 

18.09 

85.02 

18.46 

84.94 

18.83 

84.85 

19.20 

87 

88 

86.08 

18.30 

86.00 

18.67 

85.91 

19.05 

85.83 

19.42 

88 

89 

87.06 

18.50 

86.97 

18.88 

86.89 

19.26 

86.81 

19.64 

89 

90 

88.03 

18,71 

87.95 

19.10 

87.87 

19,48 

87.78 

19.86 

90 

91 

89.01 

18.92 

88  .  93 

19.31 

88.84 

19.70 

88.76 

20.08 

91 

92 

89.99 

19.13 

89.91 

19.52 

89.82 

19.91 

89.73 

20.30 

92 

93 

90.97 

19.34 

90.88 

19.73 

90.80 

20.13 

90.71 

20.52,, 

9? 

94 

91.95 

19.54 

91.86 

19.94 

91.77 

20.35 

91.68 

20.75 

94 

95 

92  .  95 

19.75 

92.84 

20  .  16 

92  .  75 

20.56 

92.66 

20  .  97 

95 

96 

93.90 

19.96 

93.81 

20.37 

93.72    20.78 

93.63 

21.19 

96 

97 

94.88 

20.17 

94.79 

20.58 

94.70 

20.99 

94.61 

21.41 

97 

98 

95.86 

20.38 

95.77 

20.79 

95.68 

21.21 

95.58 

21.63 

98 

99 

96.84 

20.58 

96.75 

21.01 

96  .  65 

21.43 

96.56 

21.85 

99 

100 

97.81 

20.79 

97.72 

21.22 

97.63 

21.64 

97.53 

22.07 

100 

aJ 
o 

c 

Dep, 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

8 

rt 

tc 

5 

78  Deg. 

77|  Deg 

77±  Deg. 

774  Deg. 

Q 

28 


TBAVFRSE    TABLE. 


G 

1 

13  Deg. 

134  Deg. 

131  rteg. 

13}  Deg. 

C 
53' 

pj 

i 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

~T 

0.97 

0.23 

0.97 

0.23 

0.97 

0.23 

0.97 

0.24 

~T 

2 

1.95 

0.45 

1.95 

0.46 

1.95 

0.47 

1.94 

0.48 

2 

3 

2.92 

0.67 

2.92 

0.69~ 

2.92 

0.70 

2.91 

0.71 

3 

4 

3.90 

0.90 

3.89 

0.92 

3.89 

0.93 

3.89 

0.95 

4 

5 

4.87 

1.12 

4.87 

1.15 

4.86 

1.17 

4.86 

1.19 

5 

6 

5.85 

1.35 

5.84 

1.38 

5.83 

1.40 

5.83 

1.43 

6 

7 

6.82 

1.57 

6.81 

1.60 

6.81 

1  .63 

6.80 

1.66 

7 

8 

7.80 

1.80 

7.79 

1.83 

7.78 

1.87 

7.77 

1.90 

8 

9 

8.77 

2.02 

8.76 

2.06 

8.75 

2.10 

8.74 

2.14 

'  9 

10 

9.74 

2.25 

9.73 

2.29 

9.72 

2.33 

9.71 

2.38 

10 

11 

10.72 

2.47 

10.71 

2.52 

10.70 

2.57 

10.68 

2.61 

11 

12 

11.69 

2.70 

11.68 

2.75 

11.67 

2.80 

11.66 

2.85 

12 

13 

12.67 

2.92 

12.65 

2.98 

12.64 

3.03 

12.63 

3.09 

13 

14 

13.64 

3.1o 

13.63 

3.21 

13.61 

3.27 

13.60 

3.33 

14 

15 

14.  62 

3.37 

14.60 

3.44 

14.59 

3.50 

14.57 

3.57 

15 

16 

15.59 

3.60 

15.57 

3.67 

15.56 

3.74 

15.54 

3.8C 

16 

17 

16.57 

3.82 

16.55 

3.90 

16.53 

3.97 

16.51 

4.04 

17 

18 

17.54 

4.05 

17.52 

4.13 

17.50 

4.20 

17.48 

4.28 

18 

19 

18.51 

4.27 

18.49 

4.35 

18.48 

4.44 

18.46 

4.52 

19 

20 

19.49 

4.50 

19.47 

4.58 

19.45 

4.67  1 

19.43 

4.75 

20 

21 

20.46 

4.72 

20.44 

4.81 

20.42 

4.90 

20.40 

4.99 

21 

22 

21.44 

4.95 

21.41 

5.04 

21.39 

5.14 

21.37 

5.23 

22 

23 

22.41 

5.17 

22.39 

5.27 

22.36 

5.37 

22.34 

5.47 

23 

24 

23.38 

5.40 

23.36 

5.50 

23.34 

5.60 

23.31 

5.70 

24 

25 

24.36 

5.62 

24.33 

5.73 

24.31 

5.84 

24.28 

5.94 

25 

26 

25.33 

5.85 

25.31 

5.96 

25.28 

6.07 

25.25   6.18 

26 

27 

26.31 

6.07 

26.28 

6.19 

26.25 

6.3-0 

26.23 

6.42 

27 

28 

27.28 

6.30 

27.25 

6.42 

27.23 

6.54 

27.20 

6.66 

28 

29 

28.26 

6.52 

28.23 

6.65 

28.20 

6.77 

28.17 

6.89 

29 

30 

29.23 

6.75 

29.20 

6.88 

29.17 

7.00 

29.14 

7.13 

30 

31 

30.21 

6.97 

30.17 

7.11 

30.14 

7.24 

30.11 

7.37 

31 

32 

31.18 

7.20 

31.15 

7.33 

31.12 

7.47 

31.08 

7.61 

32 

33 

32.15 

7.42 

32.12 

7.56 

32.09 

7.70 

32.05 

7.84 

33 

34 

33.13 

7.65 

33.09 

7.79 

33.06 

7.94 

33.03 

8.08 

34 

35 

34.10 

7.87 

34.07 

8.02 

34.03 

8.17 

34  00 

8.32 

35 

36 

35.08 

8.10 

35.04 

8.25 

35.01 

8.40 

34.97 

8.56 

36 

37 

36.05 

8.32 

36.02 

8.48 

35.98 

8.64 

35.94 

8.79 

*37 

38 

37.03 

8.55 

36.99 

8.71 

36.95 

8.87 

36.91 

9.03 

38 

39 

38.00 

8.77 

37.96 

8.94 

37.92 

9.10 

37.88 

9.27 

39 

40 

38.97 

9.00 

38  .  94 

9.17 

38.89 

9.34 

38.85 

9.51 

40 

41 

39.95 

9.22 

39.91 

9.40 

39.87 

9.57 

39.83 

9.75 

41 

42 

40.92 

9.45 

40.88 

9.63 

40.84 

9.80 

40.80 

9.98 

42 

43 

41.90 

9  67 

41.86 

9.86 

41.81 

10.04 

41.77 

10.22 

43 

44 

42.87 

9.90 

42.83 

19.08 

42.  73 

10.27 

42.74 

10.46 

44 

45 

43.85 

10.12 

43.80 

10.31 

43.76 

10.51 

43.71 

10.70 

45 

46 

44.82 

10.35 

44.78 

10.54 

44.73 

10.74 

44.68 

10.93 

46 

47 

45.80 

10.57 

45.75 

10.77 

45.70 

10.97 

45.65 

11.17 

47 

48 

46  .  77 

10.80 

46.72 

11.00 

46  .  67 

11.21 

46.62 

11.41 

48 

49 

47.74 

11.02 

47.70 

11.23 

47.65 

11.44 

47.60 

11.65 

49 

50 

48.72 

11.25 

48.67 

11.46 

48.62 

11.67 

48.57 

11.88 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

§ 

e 

c 

a 

to 

.el 

77  Deg. 

76|  Deg. 

76^  Deg. 

76i  Deg. 

1 

Q 

TRAVERSE    TABLE. 


d 

13  Deg. 

134  Deg. 

13£  Deg. 

13|  Deg. 

O 

w' 

p" 

1 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

~M 

49.69 

11.47 

49.64 

TTVeT 

49.59 

11.91 

49.54 

12.12 

51 

52 

50.67 

11.70 

50.62 

11.92 

50.56 

12.14 

50.51 

12.36 

52 

53 

51.64 

11.92 

51.59 

12.15 

51.54 

12.37 

51.48 

12.60 

53 

54 

52.62 

12.15 

52.56 

12.38 

52.51 

12.61 

52.45 

12.84 

54 

55 

53.59 

12.37 

53.54 

12.61 

53.48 

12.84 

53.42 

13.07 

55 

56 

54.56 

12.60 

54.51 

12.84 

54.45 

13.07 

54.40 

13.31 

56 

57 

55.54 

12.82 

55.48 

13.06 

55,43 

13.31 

55.37 

13.55 

57 

58 

56.51 

13.05 

56.46 

rs.29 

56.40 

13.54 

56.34 

13.79 

58 

59 

57.49 

13.27 

57.43 

13.52 

57.37 

13.77 

57.31 

14.02 

59 

60 

58.46 

13.50 

58.40 

13.75 

58.34 

14.01 

58.28 

14.26 

60 

61 

59.44 

13.72 

59.38 

13.98 

59.31 

14.24 

59.25 

14.50 

61 

62 

60.41 

13.95 

60.35 

14.21 

60.29 

14.47 

60.22 

14.74 

62 

63 

61.39 

14.17 

61.32 

14.44 

61.26 

14.71 

61.19 

14.97 

63 

64 

62.36 

14.40 

62.30 

14.67 

62.23 

14.94 

62.17 

15.21 

64 

65 

63.33 

14.62 

63.27 

14.90 

63.20 

15.17 

63.14 

15.45 

65 

66 

64.31 

14.85 

64.24 

15.13 

64.18 

15.41 

64.11 

15.69 

66 

67 

65.28 

15.07 

65.22 

15.36 

65.15 

15.64 

65.08 

15.93 

67 

68 

66.26 

15.30 

66.19 

15.59 

66.12 

15.87 

C6.05 

16.16 

68 

69 

67.23 

15.52 

67.16 

15.81 

67.09 

16.11 

67.02 

16.40 

69 

70 

68.21 

15.75 

68.14 

16.04 

68.07 

16.34 

67.99 

16.64 

70 

71 

69.18 

15.97 

69.11 

16.27 

69.04 

16.57 

68.97 

16.88 

71 

72 

70.15 

16.20 

70.08 

16.50 

70.01 

16.81 

69.94 

17.11 

72 

73 

71.13 

16.42 

71.06 

16.73 

70.98 

17.04 

70.91 

17.35 

73 

74 

72.10 

16.65 

72.03 

16.96 

71.96 

17.28 

71.88 

17.59 

74 

75 

73.08 

16.87 

73.00 

17.19 

72.93 

17.50 

72.85 

17.83 

75 

76 

74.05 

17.10 

73.98 

17.42 

73.90 

17.74 

73.82 

18.06 

76 

77 

75.03 

17.32 

74.95 

17.65 

74.87 

17.98 

74.79 

18.30 

77 

78 

76.00 

17.55 

75.92 

17.88 

75.84 

18.21 

75.76 

18.54 

78 

79 

70.98 

17.77 

76.90 

18.11 

76.82 

18.44 

76.74 

18.78 

79 

80 

77.95 

18.00 

77.87 

18.34 

77.79 

18.68 

77.71 

19.01 

80 

81 

78  .  92 

18.22 

78.84 

18.57 

78.76 

18.91 

78.68 

19.25 

81 

82 

79.90 

18.45 

79.82 

18.79 

79.73 

19.14 

79.65 

19.49 

82 

83 

80.87 

18.67 

80.79 

19.02 

80.71 

19.38 

80.62 

19.73 

83 

84 

81.85 

18.90 

81.76 

19.25 

81.68 

19.61 

81.59 

19.97 

84 

85 

82.82 

19.12 

82.74 

19.48 

82.65 

19.84 

82.56 

20.20 

85 

86 

83.80 

19.35 

83.71 

19.71 

83.62 

20.08 

83.54 

20.44 

86 

87 

84.77 

19.57 

84.68 

19.94 

84.60 

20.31 

84.51 

20.68 

87 

88 

85.74 

19.80 

85.66 

20.17 

85.57 

20.54 

85.48 

20.92 

88 

89 

86.72 

20.02 

86.63 

20.40 

86.54 

20.78 

86.45 

21.15 

89 

90 

87.69 

20.25 

87.60 

20  .  63 

87.51 

21.01 

87.42 

21.39 

90 

91 

88.67 

20.47 

88  .  58 

20.86  ! 

88.49 

21.24 

88.39 

21.63 

91 

92 

89.64 

20.70 

89.55 

21.09 

89.46 

21.48 

89.36 

21.87 

92 

93 

90.62 

20.92 

90.52 

21.32 

90.43 

21.71 

90.33 

22.10 

93 

94 

91.59 

21.15 

91.50 

21.54 

•91.40 

21.94 

91.31 

22.34 

94 

95 

92.57 

21.37 

92.47 

21.77 

92.38 

22.18 

92.28 

22.58 

95 

96 

93.54 

21.60 

93.44 

22.00  !  93.35 

22.41 

93.25 

22.82 

96 

97 

94.51 

21.82 

94.42 

22.23  I!  94.32 

22.64 

94.22 

23.06 

97 

98 

95.49 

22,05 

95.39 

22.46  I 

95.29 

22.88 

95.19 

23.29 

98 

99 

96.46 

22.27 

96.36 

22.69 

96.26 

23.11 

96.16 

23.53 

99 

100 

97.44 

22.50 

97.34 

22.92 

97.24 

23.34 

97.13 

23.77 

100 

I 

Dep.  |    Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

M 

« 

ct 

3 

77  Deg. 

76|  Deg. 

76£  Deg. 

76J  Deg. 

5 

ao 


TRAVEKsE      ABLE. 


o 

14  Deg. 

14i  Deg. 

14|  Deg. 

u{  Deg. 

O 

an' 

1 

£" 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

1 

0.97 

0.24 

0.97 

0.25 

0.97 

0.25 

0.97 

0.25 

l 

2 

1.94 

0.48 

1.94 

0.49 

1.94 

0.50 

1.93 

0.51 

2 

3 

2.91 

0.73 

2.91 

0.74 

2.90 

0.75 

2.90 

0.76 

3 

4 

3.88 

0.97 

3.88 

0.98 

3.87 

1.00 

3.87 

1.02 

4 

5 

4.85 

1.21 

4.85 

1.23 

4.84 

1.25 

4.84 

1.27 

5 

6 

5.82 

1.45 

5.82 

1.48 

5.81 

1.50 

5.80 

1.53 

6 

7 

6.79 

1.69 

6.78 

1.72 

6.78 

1.75 

6.77 

1.78 

7 

8 

7.76 

1.94 

7.75 

1.97 

7.75 

2.00 

7.74 

2.04 

8 

9  [  8.73 

2.18 

8.72 

2.22 

8.71 

2.25 

8.70 

2.29 

9 

10   9.70|  2.42 

9.69 

2.46 

9.63 

2.50 

9.67 

2.55 

10 

11  10.671  2.66 

10.66 

2.71 

10.65 

2  .  75 

10.64 

2.80 

11 

12  11.64 

2.90  j 

11.63 

2.95 

]  1  .  62 

3.00 

11.60 

3.06 

12 

13 

12.61 

3.15 

12.60 

3.20 

12.59 

3.25 

12.57 

3.31 

13 

14 

13.58 

3.39 

13.57 

3.45 

13.55 

3.51 

13.54 

3.56 

14 

15 

14.55 

3.63 

14.54 

3.69 

14.52 

3.76 

14.51 

3.82 

15 

16 

15.52 

3.87 

15.51 

3.94 

15.49 

4.01 

15.47 

4.07 

16 

17 

16.50 

4.11 

16.43 

4.18 

16.46 

4.26 

16.44 

4.33 

17 

18 

17.47 

4.35 

17.45 

4.43 

17.43 

4.51 

17.41 

4.58 

18 

19 

18.44 

4.60 

18.42 

4.63 

18.39 

4.76 

18.37 

4.84 

19 

20 

19.41 

4.84 

19.38 

4.92 

19.36 

5.01 

19.34 

5.09 

20 

21 

20.38 

5.08 

20.35 

5.17 

20.33 

5.26 

20.31 

5.35 

21 

22 

21.35 

5.32 

21.32 

5.42 

21.30 

5.51 

21.28 

5.60 

22 

23 

22.32 

5,56- 

22  .  29 

5.66 

22.27 

5.76 

22.24 

5.86 

23 

21 

23.99 

5.81 

23  .  26 

5.91 

23.24 

6.01 

23.21 

6.11 

24 

25 

24.26 

6.05 

24.23 

6.15 

24.20 

6.26 

24.18 

6.37 

25 

26 

25.23 

6.29 

25  .  20 

6.40 

25.17 

6.51 

25.14 

6.62 

26 

27 

26.20 

6.53 

26.17 

6.65 

26.14 

6.76 

26.11 

6.87 

27 

28 

27.17 

6.77 

27.14 

6.89 

27.11 

7.01 

27.03 

7.13 

28 

29 

23.14 

7.02 

28.11 

7.14 

28.08 

7.26 

23.04 

7.3S. 

29 

30 

29.11 

7.26 

29.08 

7.38 

29.04 

7.51 

29.01 

7  .  04 

30 

31 

30.08 

7.50 

30.05 

7.63 

30.01 

7.76 

29.93 

7.39 

31 

32 

31.05 

7.74 

31.02 

7.88 

30.98 

8.01 

33.95 

8.15 

32 

33 

32.02 

7.98 

31.98 

8.12 

31.95 

8.25 

31.91 

8.40 

33 

34 

32  .  99 

8.23 

32.95 

8.37 

32  92 

8.51 

32.88 

8.60 

34 

35 

33.96 

8.47 

33.92 

8.62 

33.89 

8.76 

33.85 

8.91 

35 

36 

34.93 

8.71 

34.89 

8.86 

34.85 

9.01 

34.81 

9.17 

35 

37 

35.90 

8.95 

35  .  86 

9.11 

35.82 

9.26 

35  .  78 

9.42 

37 

38 

36.87 

9.19 

36.83 

9.35 

36  .  79 

9.51 

36  .  75 

9.67 

33 

39 

37  .  84 

9.44 

37.80 

9.00 

37.76 

9.76 

37.71 

9.93 

39 

40 

33.81 

9  .  68 

38  .  77 

9.85 

33  .  73 

10.02 

33  .  63 

10.18 

40 

41 

39.78   9.92 

39  .  74 

10.09 

39  .  69 

10.27 

39  .  65 

10.44 

41 

42 

40.75  10.16 

40.71 

10.34 

40.66 

10.52 

40.62 

10.69 

42 

43 

41.72  10.40 

41.68 

10.58 

41.63 

10.77 

41.58 

10.95 

43 

44 

42.69 

10.64 

42.65 

10.83 

42.60 

11.02 

42.55 

11.20 

44 

45 

43.66 

10.89 

43  .  62 

11.03 

43.57 

11.27 

43.52 

11.46 

45 

46 

44.63!  11.13 

44.58 

1  1  .  32 

44.53 

1  1  .  52 

44.48 

11.71 

46 

47 

45.60!  11.37 

45  .  55 

1  1  .  57 

45.50 

11.77 

45.45 

11.97 

47 

48 

46.57  11.61 

46  .  52 

11.82 

46.47 

12.02 

46.42 

12.22 

48 

49 

47.54  11.85 

47.49 

12.06 

47.44 

12.27 

47.39 

12.48 

49 

50 

48.51 

12.10 

48.46 

12.31 

48.41 

12.52 

48.35 

12.73 

50 

c 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

w 

to 

1 

s 

76  Deg. 

751  Deg. 

751  Deg. 

75}  Deg. 

s 

TR« VERSE    TABLE. 


31 


d 

14  Deg. 

144  Deg. 

14£  Deg. 

14}  Deg. 

O 

1 

5" 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p 

51 

49.49 

12.34 

49.43 

12.55 

49.38 

12.77 

49.32 

12.98 

51 

52 

50.46 

12.58 

50.40 

12.80 

50.34 

13.02 

50.29 

13.24 

52 

53 

51.43 

12.82 

51.37 

13.05 

51.31 

13.27 

51.25 

13.49 

53 

54 

52.40 

13.06 

52.34 

13.29 

52.28 

13.52 

52.22 

13.75 

54 

55 

53.37 

13.31 

53.31 

13.54 

53.25 

13.77 

53.19 

14.00 

55 

56 

54.34 

13.55 

54.28 

13.78 

54.22 

14.02 

54.15 

14.26 

56 

57 

55.31 

13.79 

55.25 

14.03 

55.18 

14.27 

55.12 

14.51 

57 

58 

56.28 

14.03 

56.22 

14.28 

56.15 

14.52 

56.09 

14.77 

58 

59 

57.25 

14.27 

57.18 

14.52 

57.12 

14.77 

57.06 

15.02 

59 

60 

58.22 

14.52 

58.15 

14.77 

58.09 

15.02 

58.02 

15.28 

60 

61 

59.19 

14.76 

59.12 

15.02 

59.06 

15.27 

58.99 

15.53 

61 

62 

60.16 

15.00 

60.09 

15.26 

60.03 

15.52 

59  .  96 

15.79 

62 

63 

61.13 

15.24 

61.06 

15.51 

60.99 

15.77 

60.92 

16.04 

63 

64 

62.10 

15.48 

62.03 

15.75 

61.96 

16.02 

61.89 

16.29 

64 

65 

63.07 

15.72 

63.00 

16.00 

62.93 

16.27 

62.86 

16.55 

65 

66 

64.04 

15.97 

63.97 

16.25 

63.90 

16.53 

63.83 

16.80 

66 

67 

65.01 

16.21 

64.94 

16.49 

64.87 

16.78 

64.79 

17.06 

67 

68 

65  .  98 

16.45 

65.91 

16.74 

65.83 

17.03 

65.76 

17.31 

68 

69 

66.95 

16.69 

66.88 

16.98 

66.80 

17.28 

66.73 

17.57 

69 

70 

67.92 

16.93 

67.85 

17.23 

67.77 

17.53 

67.69 

17.82 

70 

71 

68.89 

17.18 

68.82 

17.48 

68.74 

17.78 

68.66 

18.08 

71 

72 

69.86 

17.42 

69.78 

17.72 

69.71 

18.03 

69.63 

18.33 

72 

73 

70.83 

17.66 

70.75 

17.97 

70.67 

18.28 

70.59 

18.59 

73 

74 

71.80 

17.90 

71.72 

18.22 

71.64 

18.53 

71.56 

18.84 

74 

75 

72  .  77 

18.14 

72.69 

18.46 

72.61 

18.78 

72.53 

19.10 

75 

76 

73.74 

18.39 

73.66 

18.71 

73.58 

19.03 

73.50 

19.35 

76 

77 

74.71 

18.63 

74.63 

18.95 

74.55 

19.28 

74.46 

19.60 

77 

78 

75.68 

18.87 

75.60 

19.20 

75.52 

19.53 

75.43 

19.86 

78 

79 

76.65 

19.11 

76.57 

19.45 

76.48 

19.78 

76.40 

20.11 

79 

80 

77.62 

19.35 

77.54 

19.69 

77.45 

20.03 

77.36 

20  .  37 

80 

81 

78.59 

19.60 

78.51 

19.94 

78.42 

20.28 

78.33 

20.62 

81 

82 

79.56 

19.84 

79.48 

20.18 

79.39 

20  .  53 

79.30 

20.88 

82 

83 

80.53 

20.08 

80.45 

20.43 

80.36 

20  .  78 

80.26 

21.13 

83 

84 

81.50 

20.32 

81.42 

20.68 

81.32 

21.03 

81.23 

21.39 

84 

85 

82.48 

20.56 

82.38 

20.92 

82.29 

21.28 

82.20 

21.64 

85 

86 

83.45 

20.81 

83.35 

21.17 

83.26 

21.53 

83.17 

21.90 

86 

87 

84.42 

21.05 

84.32 

21.42 

84.23 

21.78 

84.13 

22.15 

87 

88 

85  .  39 

21.29 

85  .  29 

21.66 

85.20 

22.03 

85.10 

22.41 

88 

89 

86.36 

21.53 

86.26 

21.91 

86.17 

22.28 

86.07 

22.66 

89 

90 

87.33 

21.77 

87.23 

22.15 

87.13 

22  .  53 

87.03 

22.91 

90 

91 

88.30 

22.01 

88.20 

22.40 

88.10 

22  .  78 

88.00 

23.17 

91 

92 

89.27 

22.26 

89.17 

22.65 

89.07 

23.04 

88.97 

23.42 

92 

93 

90.24 

22.50 

90.14 

22.89 

90.04 

23.29 

89.94 

23.68 

93 

94 

91.21 

22.74 

91.11 

23.14 

91.01 

23.54 

90.90 

23.93 

94 

95 

92.18 

22.98 

92.08 

23.38 

91.97 

23.79 

91.87 

24.19 

95 

96 

93.15 

23.22 

93.05 

23.63 

92.94 

24.04 

92.84 

24.44 

96 

97 

94.12 

23.47 

94.02 

23.88 

93.91 

24.29 

93.80 

24.70 

97 

98 

95.09 

23.71 

94.98 

24.12 

94.88 

24.54 

94.77 

24.95 

98 

99 

96.06 

23  9i. 

95.95 

24.37 

95.85 

24.79 

95.74 

25.21 

Q9 

100 

97.03 

24.19 

96.92 

24.62 

96.81 

25.04 

96.70 

25.46 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

S 

fl 

P 

76  Deg. 

75|  Deg. 

75i  Deg. 

75}  Deg. 

la 

Q 

TRAVERSE    TABLE. 


o 

p 

15  Deg. 

15}  Deg. 

15£  Deg. 

15|  Deg. 

O 
5" 

P 

o 
o 

Lat.  I  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 
O 

CD 

1 

0.97~ 

0.26 

0.96 

~0.26 

0.96 

0.27 

0.96 

0.27 

T 

2 

1.93 

0.52 

1.93 

0.53 

1.93 

0  .  53 

1.92 

0.54 

2 

3 

2.90 

0.78 

2.89 

0.79 

2.89 

0.80 

2.89 

0.81 

3 

4 

3.86 

1.04 

3.86 

1.05 

3.85 

1.07 

3.85 

1.09 

4 

5 

4.83 

1.29 

4.82 

1.32 

4.82 

1.34 

4.81 

1.36 

5 

6 

5.80 

1.55 

5.79 

1.58 

5.78 

1.60 

5.77 

1.63 

6 

7 

6.76 

1.81 

6.75 

1.84 

6.75 

1.87 

6.74 

1.90 

7 

8 

7.73 

2.07 

7.72 

2.10 

7.71 

2.14 

7.70 

2.17 

8 

9 

8.69 

2  .'33 

8.68 

2.37 

8.67 

2.41 

8.66 

2.44 

9 

10 

9.66 

2.59 

9.65 

2.63 

9.64 

2.67 

9.62 

2.71 

10 

11 

10.63 

2.85 

10.61 

2.89 

10.60 

2.94 

10.59 

2.99 

11 

12 

11.59 

3.11 

1  1  .  58 

3.16 

11.56 

3.21 

11.55 

3.26 

12 

13 

12.56 

3.36 

12.54 

3.42 

12.53 

3.47 

12.51 

3.53 

13 

14 

13.52 

3.62 

13.51 

3.68 

13.49 

3.74 

13.47 

3.80 

14 

15 

14.49 

3.88 

14.47 

3.95 

14.45 

4.01 

14.44 

4.07 

15 

16 

15.45 

4.14 

15.44 

4.21 

15/42 

4.28 

15.40 

4.34 

16 

17 

16.42 

4.40 

16.40 

4.47 

16.38 

4.54 

16.36 

4.61 

17 

18 

17.39 

4.68 

17.37 

4.73 

17.35 

4.81 

17.32 

4.89 

18 

19 

18.35 

4.92 

18.33 

5.00 

18.31 

5.08 

18.29 

5.16 

19 

20 

19.32 

5.18     19.30 

5.26 

19.27 

5.34 

19.25 

5.43 

20 

21 

20  .  28 

5  .44     20  .  26 

5  .  52 

20".  24 

5.61  | 

20.21 

5.70 

21 

22 

21.25 

5.69  i  21.23 

5.79 

21.20 

5.88  | 

21.17 

5.97 

22 

23 

22  .  22 

5.95     22.19 

6.0;3 

22.16 

6.15     22.14 

6.24 

23 

24 

23.18 

6.21 

23.15 

6.31 

23.13 

6.41 

23.10 

6.51 

24 

25 

24.15 

6.47 

24.12 

6.  58 

24.09 

6.68 

24.06 

6.79 

25 

26 

25  .  1  1 

6.73 

25  .  08 

6.84 

25.05 

6.95 

25.02 

7.06 

26 

27 

26.08 

6.99 

26.05 

7.10 

26.02 

7.22 

25  .  99 

7.33 

27 

28 

27  .  05 

7.25 

27.01 

7.38 

28.98 

7.48 

28.95 

7.60 

28 

29 

28.01 

7.51 

27  .  98 

7.63 

27.95 

7.75 

27.91 

7.87 

29 

30 

28  .  98 

7.76 

28  .  94 

7.89 

28.91 

8.02 

28.87 

8.14 

30 

31     29.94 

8.02 

29.91J     8.151 

29.87 

8.28 

29.84 

8.41 

31 

32 

30  .  9  1 

8.28 

30.87      8.42 

30.84 

8.55 

30.80 

8.69 

32 

33 

31.88 

8.54 

31.84 

8.68  ! 

31.80 

8.82 

31.76 

8.96 

33 

34 

32  .  84 

8,80 

32.80 

8.94 

32.76 

9.09 

32  .  72 

9.23 

34 

35 

33.81 

9.06 

33  .  77 

9.21 

33  .  73 

9.35 

33.69 

9.50 

35 

36 

34.77 

9.32 

34.73 

9.47 

34.69 

9  .  62 

34.65 

9.77 

36 

37 

35  .  74 

9.5S 

35  .  70 

9.73 

35.65 

9.89 

35.61 

10.04 

37 

38 

36.71 

9.84 

36.68 

10.00 

35.62 

10.16 

36  .  57 

10.31 

38 

39 

37.67 

10.09 

37.63 

10.26  | 

37.58 

10.42 

37  .  54 

10.59 

39 

40 

38.64 

10.35 

33  .  59 

10.52' 

33  .  55 

10.69 

38.50 

10.86 

40 

41 

39.60  !  10.61 

39.56 

10.78 

39  .  5  i 

10.96 

39.46 

11.13 

41 

42 

40.57    10.87 

40.521,  11.05 

40.47 

11.22 

40.42 

11.40 

42 

43 

41.53    11.13     41.49 

11.31 

41.44 

11.49 

41.39 

11.67 

43 

44 

42.50    11.39  !  42.45 

1  1  .  57 

42.40' 

11.76 

42.35 

11.94 

44 

45 

43.47    11.65 

43.42    11.84 

43.36 

12.03 

43.31 

12.21 

45 

46  •  44.43    11.91 

44.38    12.10 

44.33 

12.29 

44.27 

12.49 

46 

47    45.40     12.16i  45.35    12.36 

45.29 

12.56 

45.24 

12.76 

47 

48    46.36 

12.42:146.31     12.63 

46.25 

12.83 

46.20    13.03 

48 

49 

47.33 

12.68:47.27    12.89 

47.22- 

13.09 

47.16    13.30 

49 

50 

48.30     12.  94i  48.  24    13.15 

48.18 

13.36 

48.12     13.57 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

0> 

a 

JH 

j| 

5 

75  Deg.              74    Deg. 

74±  Deg. 

74}  Deg. 

•s 

O 

TH AVERSE   TABLE. 


0 

15  Deg. 

15$  Deg. 

15|  Deg. 

15|  Deg. 

O 

p" 

?» 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

51 

49.26 

13.20 

49.20 

13.41 

49.15 

13.63 

49.09 

13.84 

51 

52 

50  .  23 

13.46 

50.17 

13.68 

50  .  1  1 

13.90 

50.05 

14.11 

52 

53  151.19 

13.72 

51.13 

13.94 

51.07 

14.16 

51.01 

14.39 

53 

54 

52.16 

13.98 

52.10 

14.20 

52.04 

14.43 

51.97 

14.66 

54 

55 

53.13 

14.24 

53.06 

14.47 

53.00 

14.70 

52  .  94 

14.93 

55 

56 

54.09 

14.49 

54.03 

J4.73 

53.96 

14.97 

53  .  90 

15.20 

56 

57 

55.06 

14.751 

54.99 

14.99 

54.93 

15.23 

54.86 

15.47 

57 

58 

56.02 

15.01 

55.96 

15.26 

55.89 

15.50 

55.82 

15.74 

58 

59 

56  .  99 

15.27 

56.92 

15.52 

56.85 

15.77 

56  .  78 

16.01 

59 

60 

57.96 

15.53 

57.89 

15.78 

57.82 

16.03 

57  .  75 

16.29 

60 

61 

58.92 

15.79 

58  ,  85 

16.04 

58.78 

16.30 

58.71 

16.56 

61 

62 

59.89 

16.05 

59.82 

16.31 

59  .  75 

16.57 

59.67 

16.83 

62 

63 

60.85 

16.31 

60.78 

16.57 

60.71 

16.84 

60.63 

17.10 

63 

64 

61.82 

16.56 

61.75 

16.83 

61.67 

17.10 

61.60 

17.37 

64 

65 

62.79 

16.82 

62.71 

17.10 

62.64 

17.37 

62.56 

17.64 

65 

66 

63.75 

17.08 

63.68 

17.35 

63  .  60 

17.64 

63.52 

17.92 

66 

67 

64.72 

17.34 

64.64 

17.62 

64.56 

17.90 

64.48 

18.19 

67 

68 

65.68 

17.60 

65.61 

17.89 

65  .  53 

18.17 

65.45 

18.46 

68 

69 

66  .  65 

17.86 

66.57 

18.15 

66.49 

18.44 

66.41 

1  8  .  73 

69 

70 

67.61 

18.12 

67.54 

18.41 

67.45 

18.71 

67.37 

19.00 

70 

71 

68.58 

18.38 

68  .  50 

18.68 

68.42 

18.97 

68.33 

19.27 

71 

72 

69  .  55 

18.63 

69.46 

18.94 

69.38 

19.24 

69.30  19.54 

72 

73 

70.51 

18.89 

70.43 

19.20 

70.35 

19.51 

70.26 

19.82 

73 

74 

71.48 

19.15 

71.39 

19.46 

71.31 

19.78 

71.22 

20.09 

74 

75 

72.44 

19.41 

72  .  36 

19.73 

72.27 

20.04 

72.18 

20.36 

75 

76 

73.41 

19.67 

73  .  32 

19.99 

73  .  24 

20.31 

73.15 

20  .  63 

76 

77 

74.38 

19.93 

74.29 

20  .  25 

74.20 

20  .  58 

74.11 

20.90 

77 

78 

75  .  34 

20.19 

75.25 

20.52  1  75.16 

20.84 

75.07 

21.17 

78 

79 

76.31 

20.45 

76  .  22 

20.78  76.13 

21.11 

76.03 

21.44 

79 

80 

77.27 

20.71 

77.18 

21.04  1  77.09 

21.38 

77.00 

21.72',  80 

81 

78.24 

20.96 

78.15 

21.31 

78.05 

21.65 

77.96 

21.99   .81 

82 

79.21 

21.22 

79.11 

21.57 

79.02 

21.91 

78  .  92 

22.26 

82 

83 

80.17 

21.48 

80.08 

21.83 

79.98 

22.18 

79  .  88 

22  .  53 

83 

84 

81.14 

21.74 

81.04 

22.09 

80.94 

22.45 

80.85 

22.80 

84 

85 

82.10 

22.00 

82.01 

22.36 

81.91 

22  .  72 

81.81 

23.07 

85 

86 

83.07 

22.26 

82.97 

22  .  62 

82.87 

22.98 

82  .  77 

23.34 

86 

87 

84.04 

22.52 

83.94 

22.88 

83.84 

23.25 

83.73 

23.62 

87 

88 

85.00 

22.78 

84.90 

23.15 

84.80 

23  .  52 

84.70 

23.89 

88 

89 

85  .  97 

23.03 

85.87 

23.41 

85.76 

23.78 

85  .  66 

24.16 

89 

90 

86  .  93 

23.29 

86.83 

23.67 

86  .  73 

24.05 

86.62 

24.43 

90 

91 

87.90 

23  .  55 

87.80 

23.94 

87.69 

24.32 

87.58 

24.70 

91 

92 

88.87 

23.81 

88  .  76 

24.20 

88  .  65 

24  .  59 

88.55 

24.97 

92 

93 

89.83 

24.07 

89  .  73 

24.46 

89  .  62 

24.85 

89.51 

25.24 

93 

94 

90.80 

24.33 

90.69 

24  .  72 

90  .  58 

25.12 

90.47 

25  .  52 

94 

95 

91.76 

24.59 

91.65 

24.99 

91.54 

25  .  39 

91.43 

25.79 

95 

96 

92.73 

24.85 

92.62 

25.25 

92.51 

25.65 

92.40 

26.06 

96 

97 

93.69 

25  .  1  1 

93.58 

25.51 

93.47 

25  .  92 

93  .  36 

26  .  33 

97 

98 

94.66 

25.36 

94  .  55 

25.78 

94.44 

26.19 

94.32 

26.60 

98 

99 

95  .  63 

25.62  95.51 

26.04 

95.40 

26.46 

95.28 

26.87 

99 

100 

96.59 

25.88 

96.48 

26.30 

96.36 

26.72 

96  .  25 

27.14 

100 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

to 

o 
fl 

.9 

fi 

75  Deg. 

-  74|  Deg. 

74i  Deg. 

74*  Deg. 

is 

Q 

34 


TRAVERSE    TABLE. 


o 
1 

16  Deg. 

164  Deg. 

161  Deg. 

16|  Deg. 

g 

1 



1 

0 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

~T  |~0  796" 

0.28 

0.96 

0.28 

0.96 

0.28 

6.96 

0.29 

f 

2   1  92 

0.55 

1.92 

0.56 

1.92 

0.57 

1.92 

0.58 

2 

3 

2.88 

0.83 

2.88 

0.84 

2.88 

0.85 

2.87 

0.86 

3 

4 

3.85 

1.10 

3.84 

1.12 

3.84 

1.14 

3.83 

1.15 

4 

5 

4.81 

1.38 

4.80 

1.40 

4.79 

1.42 

4.79 

1.44 

5 

6 

5.77 

1.65 

5.76 

1.68 

5.75 

1.70 

5.75 

1.73 

6 

7 

6.73 

1.93 

6.72 

1.96 

6.71 

1.99 

6.70 

2.02 

7 

8 

7.69 

2.21 

7.68 

2.24 

7.67 

2.27 

7.66 

2.31 

8 

9 

8.65 

2.48 

8.64 

2.52 

8.63 

2.56 

8.62 

2.59 

9 

10 

9.61 

2.76 

9.60 

2.80 

9.59 

2.84 

9.58 

2.88 

10 

11 

10.57 

3.03 

10.56 

3.08 

10.55 

3.12 

10.53 

3.17 

11 

12 

11.54 

3.31 

11.52 

3.36 

11.51 

3.41 

11.49 

3.46  I  12 

13 

12.50 

3.58 

12.48 

3.64 

12.46 

3.69 

12.45 

3.75 

13 

14 

13.46 

3.86 

13.44 

3.92 

13.42 

3.98 

13.41 

4.03 

14 

15 

14.42 

4.13 

14.40 

4.20 

14.38 

4.26 

14.36 

4.32 

15 

16 

15.38 

4.41 

15.36 

4.48 

15.34 

4.54 

15.32 

4.61 

16 

17 

16.34 

4.69 

16.32 

4.76 

16.30 

4.83 

16.28 

4.90 

17 

18 

17.30 

4.96 

17.28 

5.04 

17.26 

5.11 

17.24 

5.19 

18 

19 

18.26 

5.24 

18.24 

5.32 

18.22 

5.40 

18.19 

5.48 

19 

20 

19.23 

5.51 

19.20 

5.60 

19.18 

5.68 

19.15 

5.76 

20 

21 

20.19 

5.79 

20.16 

5.88 

20.14 

5.96 

20.11 

6.05 

21 

22 

21.15 

6.06 

21.12 

6.16 

21.09 

6.25 

21.07 

6.34 

22 

23 

22  .  1  1 

6.34 

22.08 

6.44 

22.05 

6.53 

22.02 

6.63 

23 

24 

23  .  07 

6.62 

23.04 

6.72 

23.01 

6.82 

22  .  98 

6.92 

24 

25 

24.03 

6.89 

24.00 

7.00 

23  .  97 

7.10 

23.94 

7.20 

25 

26 

24.99 

7.17 

24.96 

7.28 

24.93 

7.38 

24.90 

7.49 

26 

27 

25.95 

7.44 

25.92 

7.56 

25.89 

7.67 

25.85 

7.78 

27 

28 

26  .  92 

7.72 

26.88 

7.84 

26.85 

7.95 

26.81 

8.07 

28 

29 

27.88 

7.99 

27.84 

8.11 

27.81 

8.24 

27.77 

8.36 

29 

30 

28  .  84 

8.27 

28.80 

8.39 

28.76 

8.52 

28.73 

8.65 

30 

31 

29.80 

8.54 

29  .  76 

8.67 

29.72 

8.80 

29.68 

8.93 

31 

32 

30  .  76 

8.82 

30.72 

8.95 

30.68 

9.09 

30.64 

9.22 

32 

33 

31.72 

9.10 

31.68 

9.23 

31.64 

9.37 

31.60 

9.51 

33 

34 

32  .  68 

9.37 

32  .  64 

9.51 

32.60 

9.66 

32.56 

9.80 

34 

35 

33  .  64 

9.65 

33.60 

9.79 

33  .  56 

9.94 

33.51 

10.09 

35 

36 

34.61 

9.92 

34.56 

10.07 

34.52 

10.22 

34.47 

10.38 

36 

37 

35.57 

10.20 

35  .  52 

10.35 

35.48 

10.51 

35.43 

10.66 

37 

38 

36  .  53 

10.47 

36.48 

10.63 

36.44 

10.79 

36.39 

10.95 

38 

39 

37.49 

10.75 

37.44 

10.91 

37.39 

11.08 

37.35 

11.24 

39 

40 

33.45 

11.03 

38.40 

11.19 

38  .  35 

11.36 

38.30 

11.53 

40 

41 

39.41 

11.30 

39.36 

"11.47 

39.31 

11.61 

39.26 

11.82 

41 

42 

40.37 

11.58 

40.32 

1  1  .  75 

40.27 

11.93 

40.22 

12.10 

42 

43 

41.33 

11.85 

41.28 

12.03 

41.23 

12.21 

41.18 

12.39 

43 

44 

42.30 

12.13 

42.24 

12.31 

42.19 

12.50 

42.13 

12.68 

44 

45 

43.26 

12.40 

43.20 

12.59 

43.15 

12.78 

43.09 

12.97 

45 

46 

41.22 

12.68 

44.16 

12.87 

44.11 

13.06 

44.05 

13.26 

46 

47 

45.18 

12.95 

45.12 

13.15 

45.06 

13.35 

45.01 

13.55 

47 

48 

46.14 

13.23 

46.08 

13.43 

46.02 

13.63 

45  .  96 

13.83 

48 

49 

47.10 

13.51 

47.04 

13.71 

46.98 

13.92 

46  .  92 

14.12 

49 

50 

48.08 

13.78 

48.00 

13.99 

47.94 

14.20 

47.88 

14.41 

50 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

03 
O 

c 

§ 

74  Deg. 

73|  Deg. 

73|  Deg. 

734  Deg. 

I 

TRAVERSE    TABLE 


35 


d 

5s 

16  Deg. 

164  Deg, 

16|  Deg. 

161  Deg. 

O 

3 
O 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I 

51 

49.02 

14.06 

48.96 

14.27 

48  .  90 

14.48 

48.84 

14.70 

51 

52 

49.99 

14.33 

49.92 

14.55 

49.86 

14.77 

49  .  79 

14.99 

52 

53 

50.95 

14.61 

50.88 

14.83 

50.82 

15.05 

50,75 

15.27 

53 

54 

51.91 

14.88 

51.84 

15.11 

51.78 

15,34 

51.71 

15.56 

54 

55 

52.87 

15.16 

52.80 

15.39 

52.74 

15.62 

52.67 

15,85 

55 

56 

53.83 

15.44 

53.76 

15.67 

53  .  69 

15.90 

53  .  62 

16.14 

56 

57 

54  .  79 

15.71 

54.72 

1^5.95 

54.65 

16,19 

54.58 

16.43 

57 

58 

55.75 

15.99 

55.68 

16.23 

55.61 

16.47 

55.54 

16.72 

58 

59 

56.71 

16.26 

56  .  64 

16.51 

56.57 

16,76 

56.50 

17.00 

59 

60 

57.68 

16.54, 

57.60 

16.79 

57.53 

17.04  J57,45 

17.29 

60 

61 

58  .  64 

16.81 

58.56 

17.07 

58.49  17.32  !  58.41 

17.58 

61 

62 

59.60 

17.09 

59  .  52 

17.35 

59.45  17,61 

59.37 

17.87 

62 

63 

60  .  56 

17.37 

60.48 

17.63 

60.41 

17.89 

60.33 

18.16 

63 

64 

6  1  .  52 

17.64 

61.44 

17.91. 

61.36 

18.18 

61.28 

18.44 

64 

65 

62.48 

17.92 

62.40 

18.19 

62.32 

18.46 

62.24 

18.73 

65 

66 

63.44 

18.19 

63.36 

18.47 

63.28 

18,74 

63.20 

19.02 

66 

67 

64.40 

18.47 

64.32 

18.75 

64.24 

19.03 

64.16 

19.31 

67 

68 

65.37 

18.74 

65.28 

19.03 

65.20 

19.31 

65  .  1  1 

19.60 

68 

69 

66.33 

19.02 

66.24 

19.31 

66.16 

19.60 

66.07 

19.89 

69 

70 

67.29 

19.29 

67.20 

19.59 

67.12 

19.88 

67.03 

20.17 

70 

~7l 

68.25 

19.57 

68.  16 

19.87 

68.08 

20  .  1  7 

67.99 

20.46 

71 

72 

69.21 

19.85 

69.12 

20.15 

69.03 

20.45 

68  .  95 

20.75 

72 

73 

70.17 

20.12 

70.08 

20.43 

69  .  99 

20.73 

69  .  90 

21.04 

73 

74 

71.13 

20.40 

71.04 

20.71 

70  .  95 

21.02 

70.86 

21.33 

74 

75 

72.09 

20.67 

72.00 

20.99 

71.91 

21.30 

71.82 

21.61 

75 

76 

73.06 

20.1/5 

72.96 

21.27 

72.87 

21.59 

72.78 

21.90 

76 

77 

74.02 

21.22 

73.92 

21.55 

73.83 

21.87  '  73.73 

22.19 

77 

78 

74.98 

21.50 

74.88 

21.83 

74  .  79 

22.15  174.69 

22.48 

78 

79 

75  .  94 

2  1  .  78 

75.84 

22.11 

75  .  75 

22.  44  fl  75.  65 

22.77 

79 

80 

76  .  90 

22.05 

76.80 

22.39 

76.71 

22.72  j  76.61 

23.06 

80 

81 

77.86 

22  .  33 

77.76 

22.67 

77.66 

23.01 

'  77  .  56 

23.34 

81 

82 

78.82 

22  .  60 

78.72 

22.95 

78.62 

23.29 

I  78.52 

23.63 

82 

83 

79  .  78 

22.88 

79  .  68 

23.23 

79  .  58 

23.57 

I  79.4-8 

23.92 

83 

84 

80  .  75 

23.15 

80.64 

23.51 

80  .  54 

23.86 

80.44 

24.21 

84 

85 

81.71 

23.43 

81.60 

23.79 

81.50 

24.14 

81.39 

24.53 

85 

86 

82.67 

23.70 

82.56 

24.07 

82.46 

24.43 

'82.35 

24.78 

86 

87 

83.63 

23.98 

83.52 

24.35 

83.42 

24.71 

183.31 

25.07 

87 

88 

84.59 

24.26 

84.48 

24.62 

84.38 

24.99 

184.27 

25,36 

88 

89 

85.55 

24.53 

85.44 

24.90 

85.33 

25  .  28 

185.22 

25.65 

89 

90 

80.51  24.81 

86.40 

25.18 

86.29 

25.56  j  86.  18 

25.94 

90 

91 

87.47 

25.08 

87.36 

25.46 

87.25 

25.85  T87.14 

26.23 

91 

92 

88.44 

25  .  36 

88.32 

25.74 

88.21 

26.13  J88.10 

26.51 

92 

93 

89.40 

25  .  63 

89.28 

26.02 

89.17 

26.41  89.05 

26.80 

93 

94 

90.36 

25.91 

90.24 

26.30 

90.13 

26.70  90.01 

27.09 

94 

95 

91.32 

26.19 

91.20 

26.58 

91.09 

26.98  90.97 

27  .  38 

95 

96 

92.28 

26.46 

92.16 

26.86 

92.05 

27.27  91.93 

27.67 

96 

97 

93.24 

26.74 

93.12 

27.14 

93.01 

27.55  92.88 

27.95 

97 

98 

94.20 

27.01 

94.08 

27.42 

93.96 

27.83  93.84 

28.24 

98 

99 

95.16 

27.29 

95.04 

27.70 

94.92 

28.12  94.80 

28.53 

99 

100 

96.13 

27.56 

96.00 

27.98 

95.88 

28.40  95.76 

28.82 

100 

o 

o 
C 

Dep. 

Lat. 

Dep.  1  Lat. 

Dep. 

Lat.  1  Dep. 

Lat. 

i 

"w 

II 

ed 
tc 

3 

74  Deg. 

73|  Deg. 

73|  Deg.     73i  Deg. 

3 

36 


TBAVERSE    TABLE. 


1 

17  Deg. 

17*  Deg. 

17£  Deg. 

17|  Deg. 

O 
53' 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 
o 

1 

0.96 

0.29 

0.95 

0.30 

0.95 

0.30 

0.95 

0.30 

I 

2 

1.91 

0.58 

1.91 

0.59 

1.91 

0.60 

1.90 

0.61 

o 

3 

2.87 

0.88 

2.87 

0.89 

2.86 

0.90 

2.86 

0.91 

3 

4 

3.83 

1.17 

3.82 

1.19 

3.81 

1.20 

3.81 

1.22 

4 

5 

4.78 

1.46 

4.78 

1.48 

4.77 

1.50 

4.76 

1.52 

5 

6 

5.74 

1.75 

5.73 

1.78 

5.72 

1.80 

5.71 

1.83 

6 

7 

6.69 

2.05 

6.69 

2.08 

6.68 

2.10 

6.67 

2  13 

7 

8 

7.65 

2.34 

7.64 

2.37 

7.63 

2.41 

7.62 

2.44 

8 

9 

8.61 

2.63 

8.60 

2.67 

8.58 

2.71 

8.57 

2.74 

9 

10 

9.56 

2.92 

9.55 

2.97 

9.54 

3.01 

9.52 

3.05 

10 

11 

10.52 

3.22 

10.51 

3.26 

10.49 

3.31 

10.48 

3.35 

11 

12 

11.48 

3.51 

11.46 

3.56 

11.44 

3.61 

11.43 

3.66 

12 

13 

12.43 

3.80 

12.42 

3.85 

12.40 

3.91 

12.38 

3.96 

13 

14 

13.39 

4.09 

13.37 

4.15 

13.35 

4.21 

13.33 

4.27 

14 

15 

14.34 

4.39 

14.33 

4.45 

14.31 

4.51 

14.29 

4.57 

15 

16 

15.30 

4.68 

15.28 

4.74 

15.26 

4.81 

15.24 

4.88 

16 

17 

16.26 

4.97 

16.24 

5.04 

16.21 

5.11 

16.19 

5.18 

17 

18 

17.21 

5.26 

17.19 

5.34 

17.17 

5.41 

17.14 

5.49 

18 

19 

18.17 

5.56 

18.15 

5.63 

18.12 

5.71 

18.10 

5.79 

19 

20 

19.13 

5.85 

19.10 

5.93 

19.07 

6.01 

19.05 

6.10 

20 

21 

20.08 

6.14 

20.06 

6.23 

20.03 

6.31 

20.00 

6.40 

2f 

22 

21.04 

6.43 

21.01 

6.52 

20.98 

6.62 

20.95 

6.71 

22 

23 

21.99 

6.72 

21.97 

6.82 

21.94 

6.92 

21.91 

7.01 

23 

24 

22.95 

7.02 

22.92 

7.12 

22.89 

7.22 

22.86 

7.32 

24 

25 

23.91 

7.31 

23.88 

7.41 

23.84 

7.52 

23.81 

7.62 

25 

26 

24.86 

7.60 

24.83 

7.71 

24.80 

7.82 

24.76 

7.93 

26 

27 

25.82 

7.89 

25.79 

8.01 

25.75 

8.12 

25.71 

8.23 

27 

28 

26.78 

8.19 

26.74 

8.30 

26.70 

8.42 

26.67 

8.54 

28 

29 

27.73 

8.48 

27.70 

8.60 

27.66 

8.72 

27.62 

8.84 

29 

30 

28  .  69 

8.77 

28.65 

8.90 

28.61 

9.02 

28.57 

9.15 

30 

31 

29.65 

9.06 

29.61 

9.19 

29  .  57 

9.32 

29.52 

9.45 

31 

32 

30.60 

9.36 

30.56 

9.49 

30.52 

9.62 

30.48 

9.76 

32 

33 

31.56 

9.65 

31.52 

9.79 

31.4.7 

9.92 

31.43 

10.06 

33 

34 

32.51 

9.94 

32.47 

10.08 

32.43 

10.22 

32.38 

10.37 

34 

35 

33.47 

10.23 

33.43 

10.38 

33.38 

10.52 

33.33 

10.67 

35 

36 

34.43 

10.53 

34.38 

10.68 

34.33 

10.83 

34.29 

10.98 

36 

37 

35.38 

10.82 

35.34 

10.97 

35.29 

11.13 

35  24 

11.28 

37 

38 

36.34 

11.11 

36.29 

11.27 

36.24 

11.43 

36.19  I  11.58 

38 

39 

37.30 

11.40 

37.25 

1  1  .  57 

37.19 

11.73 

37.14 

11.89 

39 

40 

38.25  11.69 

38.20 

11.86 

38.15 

12.03 

38.10 

12.19 

40 

41 

39.21 

11.99 

39.16 

12.16 

39.10 

12.33 

39.05 

12.50 

41 

42 

40.16 

12.28 

40.11 

12.45 

40.06 

12.63 

40.00 

12.80 

42 

43 

41.12 

12.57 

41.07 

12.75 

41.01 

12.93 

40.95 

13.11 

43 

44 

42.08 

12.86 

42.02 

13.05 

41.96 

13.23 

41.91 

13.41 

44 

45 

43.03 

13.16 

42.98 

13.34 

42.92 

13.53 

42.86 

13.72 

45 

46 

43.99 

13.45 

43.93 

13.64 

43.87 

13.83 

43.81 

14.02 

46 

47 

44.951  13.74 

44.89 

13.94 

44.82 

14.13 

44.76 

14.33 

47 

48 

45.90 

14.03 

45.84 

14.23 

45.78 

14.43 

45.71 

14.63 

48 

49 

46.86 

14.33 

46.80 

14.53 

46.73 

14.73 

46.67 

14.94 

49 

50 

47.82 

14.62 

47.75 

14.83 

47.69 

15.04 

47.62 

15.24 

50 

§ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

oJ 
o 

B 

a 

3 

rf 

09 

c 

73  Deg. 

72|  Deg. 

72£  Deg. 

72i  Dag. 

Q 

TKAVERSE    TABLE, 


37 


o 

17  Deg. 

17}  Deg. 

17£  Deg. 

17|  Deg. 

O 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

51 

48.77 

14.91 

48.71 

15.12 

48.64 

15.34 

48.57 

15.55 

51 

52 

49.73 

15.20 

49.66 

15.42 

49.59 

15.64 

49.52 

15.85 

52 

53 

50.68 

15.50 

50.62 

15.72 

50.55 

15.94 

50.48 

16.16 

53 

54 

51.64 

15.79 

51.57 

16.01 

51.50 

16.24 

51.43 

16.46 

54 

55 

52.60 

16.08 

52.53 

16.31 

52.45 

16.54 

52.38 

16.77 

55 

56 

53.55 

16.37 

53.48 

16.61 

53.41 

16.84 

53.33 

17.07 

56 

57 

54.51 

16.67 

54.44 

1'6.90 

54.36 

17.14 

54.29 

17.38 

57 

58, 

55.47 

16.96 

55.39 

17.20 

55.32 

17.44 

55.24 

17.68 

58 

59 

56.42 

17.25 

56.35 

17.50 

56.27 

17.74 

56.10 

17.99 

59 

60 

57.38 

17.54 

57.30 

17.79 

57.22 

18.04 

57.14 

18.29 

60 

61 

58733 

17.83 

58.26 

18.09 

58.18 

18.34 

58.10 

18.60 

61 

62 

59.29 

18.13 

59.21 

18.39 

59.13 

18.64 

59.05 

18.90 

62 

63 

60.25 

18.42 

60.17 

18.68 

60.08 

18.94 

60.00 

19.21 

63 

64 

61.20 

18.71 

61.12 

18.98 

61,04 

19.25 

60.95 

19.51 

64 

65 

62.16 

19.00 

62.08 

19.28 

61.99 

19.55 

61.91 

19.82 

65 

66 

63.12 

19.30 

63.03 

19.57 

62.95 

19.85 

62.86 

20.12 

66 

67 

64.07 

19.59 

63.99 

19.87 

63.90 

20.15 

63.81 

20.43 

67 

68 

65.03 

19.88 

64.94 

20.16 

64.85 

20.45 

64.76 

20.73 

68 

69 

65.99 

20.17 

65.90 

20.46 

65.81 

20.75 

65.72 

21.04 

69 

70 

66.94 

20.47 

66.85 

20.76 

66.76 

21.05 

66.67 

21.34 

70 

71 

67,90 

20  .  76 

67.81 

21.05 

67.71 

21.35 

67.62 

21.65 

71 

72 

68.85 

21.05 

68.76 

21.35 

68.67 

21.65 

68.57 

21.95 

72 

73 

69.81 

21.34 

69.72 

21.65 

69.62 

21.95 

69.52 

22.26 

73 

74 

70.77 

21.64 

70.67 

21.94 

70.58 

22.25 

70.48 

22.56 

74 

75 

71.72 

21.93 

71.63 

22,24 

71.53 

22.55 

71.43 

22.86 

75 

76 

72.68 

22.22 

72.58 

22.54 

72.48 

22.85 

72.38 

23.17 

76 

77 

73.64 

22.51 

73.54 

22.83 

73.44 

23.15 

73.33 

23.47 

77 

78 

74.59 

22.80 

74.49 

23.13 

74.39 

23.46 

74.29 

23.78 

78 

79 

75.55 

23.10 

75.45 

23.43 

75.34 

23.76 

75.24 

24.08 

79 

80 

76.50 

23.39 

76.40 

23.72 

76.30 

24.06 

76.19 

24.39 

80 

81 

77.46 

23.68 

77.36 

24.02 

77.25 

24.36 

77.14 

24.69 

81 

82 

78.42 

23.97 

78.31 

24.32 

78.20 

24.66 

78.10 

25.00 

82 

83 

79.37 

24.27 

79.27 

24.61 

79.16 

25.96 

79.05 

25.30 

83 

84 

80.33 

24.56 

80'.  22 

24.91 

80.11 

25.26 

80.00 

25.61 

84 

85 

81.29 

24.85 

81.18 

25.21  181.07 

25.56 

80.95 

25.91 

85 

86 

82.24 

25.14 

82.13 

25.50    82.02 

25.86 

81.91 

26.22 

86 

87 

83.20 

25.44 

83.09 

25.80     82.97 

26.16 

82.86 

26.52 

87 

88 

84.15 

25.73 

84.04 

26.10     83.93 

26.46 

83.81 

26.83 

88 

89 

85.11 

26.02 

85.00 

26.39!  84.88 

26.76 

84.76 

27.13 

89 

90 

86.07 

26.31 

85.95 

26.69  !  85.83 

27.06 

85.72 

27.44 

90 

91 

87.02 

26.61 

86.91 

26.99  i  86.79 

27.36 

86.67 

27.74 

91 

92 

87.98 

26.90 

87.86 

27.28  ,  87.74 

27.66 

87.62 

28.05 

92 

93 

88.94 

27.19 

88.82 

27.58     88.70 

27.97 

88.57 

28.35 

93 

94 

89.89 

27.48 

89.77 

27.87  i  89.65 

28.27 

89.53 

28.66 

94 

95 

90.85 

27.78 

90,73 

28.17  j  90.  60 

28,57 

90.48 

28.96 

95 

96 

91.81 

28.07 

91.68 

28.47  I  91.56 

28.87 

91.43 

29.27 

96 

97 

92.76 

28.36 

92.64 

28.76 

92.51 

29.17 

92.38 

29.57 

97 

98 

93.72 

28.65 

93.59 

29.06 

93.46 

29.47 

93.33 

29.88 

98 

99 

94.67 

28.94 

94.55 

29.39 

94.42 

29.77 

94.29 

30.18 

99 

100 

95.63 

29.24 

35.50 

29.65 

95.37 

30.07 

95.24 

30.49 

100 

I 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

o 

c 

I 

*s 

Q 

73  Deg. 

72J  Deg. 

72£  Deg. 

72i  Deg. 

S 

TRAVERSE    TABLE, 


g 

18  Deg. 

18*  Deg. 

18|  Deg. 

181  Deg. 

g 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1 

0.95 

0.31 

0.95 

0.31 

0.95 

0.32 

0.95 

0.32 

1 

2 

1.90 

0.62 

1.90 

0.63 

1.90 

0.63 

1.8ft 

0.64 

2 

3 

2.85 

0.93 

2.85 

0.94 

2.84 

0.95 

2.84 

0.96 

3 

4 

3.80 

1.24 

3.80 

1.25 

3.79 

1.27 

3.79 

1.29 

4 

5 

4.76 

1.55 

4.75 

1.57 

4.74 

1.59 

4.73 

1.61 

5 

6 

5.71 

1.85 

5.70 

1.88 

5.69 

1.90 

5.68 

1.93 

6 

7 

6.66 

2.16 

6  .  65 

2.19 

6.64 

2.22 

6.63 

2.25 

7 

8 

7.61 

2.47 

7.60 

2.51 

7.59 

2.54 

7.58 

2.5? 

8 

9 

8.56 

2.78 

8.55 

2.82 

8.53 

2.86 

8.52 

2.89 

9 

10 

9.51 

3.09 

9.50 

3.13 

9.48 

3.17 

9.47 

3.21 

10 

11 

10.46 

3.40 

10.45 

3.44 

10.43 

3.49 

10.42 

3.54 

11 

12 

11.41 

3.71 

11.40 

3.76 

11.38 

3.81 

11.36 

;3.86 

12 

13 

12.36 

4.02 

12.35 

4.07 

12.33 

4.12 

12.31 

4.18 

13 

14 

13.31 

4.33 

13.30 

4.38 

13.28 

4.44 

13.2-6 

4.50 

14 

15 

14.27 

4.64 

14.25 

4.70 

14.22 

4.76 

14.20 

4.82 

15 

16 

15.2? 

4.94 

15.20 

5.01 

15.17 

5.03 

15.15 

5.14 

16 

17 

16.17 

5.25 

16.14 

5.32 

16.12 

5.39 

16.10 

5.46 

17 

18 

17.12 

5.56 

17.09 

5.64 

17.07 

5.71 

17.04 

5.79 

18 

19 

18.07 

5.87 

18.04 

5.95 

18.02 

6.03 

17.99 

6.11 

19 

20 

19.02 

6.18 

18.99 

6.26 

18.97 

6.35 

18.94 

6.43 

20 

21 

19.97 

6.49 

19.94 

6.58 

19.91 

6.66 

19.89 

6.75 

21 

22 

20.92 

6.80 

20.89 

6.89 

20.86 

6.98 

243.83 

7.07 

22 

23 

21.87 

7.11 

21.84 

7.20 

21.81 

7.30 

21.78 

7.39 

23 

24 

22.83 

7.42 

22.79 

7.52 

22  .  76 

7.62 

22.73 

7.71 

24 

25 

23.78 

7.73 

23.74 

7.83 

23.71 

7.93 

23.67 

8.04 

25 

26 

24.73 

8.03 

24.69 

8.14 

24.66 

8.25 

24.62 

8.36 

26 

27 

25.68 

8.34 

25.64 

8.46 

25.60 

8.57 

25.57 

8.68 

27 

28 

26.63 

8.65 

26.59 

8.77 

26.55 

8.88 

26.51 

».op 

28 

29 

27.58 

8.96 

27.54 

9.08 

27.50 

9.20 

27.  4S 

9.32     29 

30 

28.53 

9.27 

28.49 

9.39 

28.45 

9.52 

28.41 

9.64 

30 

~3T 

29.48 

9.58 

29.44 

9.71  '. 

29.40 

9.84 

29.35 

9.96 

31 

32 

30.43 

9.89 

30.39 

10.02 

30.35 

10.15 

30.30 

10.29 

32 

33 

31.38 

10.20 

31.34 

10.33  ( 

31.29 

10.47 

31.25 

10.61 

33 

34 

32.34 

JO.  51 

32.29 

10.65  t 

32  .  24 

10.79 

32  .  20 

10.93 

34 

35 

33.29 

10.82 

33.24 

10.96 

33.19 

11.11 

33.14 

11.25 

35 

36 

34.24 

11.12 

34.19 

11.27 

34.14 

11.42 

34.09 

1  1  .  57 

36 

37 

35.19 

11.43 

35.14 

11.59 

35.09 

1  1  .  74 

35.04 

11.89 

37 

38 

36.14 

1  1  .  74 

36.09 

11.90 

36.04 

12.00 

35.98 

12.21 

38 

39, 

37.09 

12.05 

37.04 

12.21  ', 

36.98 

12.37 

36  .  93 

12.54 

39 

40 

38.04 

1  2  .  36 

37.99 

12.53 

37.93 

12.69 

37.88 

12.86 

40 

41 

38.99 

12.67 

38.94 

12.84 

38.88 

13.01 

38.82 

13.18 

41 

42 

39.94 

12.98 

39.89 

13.15 

39.83 

13.33 

39.77 

13.50 

42 

43 

40.90 

13.29 

40.84 

13.47 

40.78     13.64 

40.72 

13.82 

43 

44 

41.85 

13.60 

41.79 

13.78 

41.73 

13.96 

41.66 

14.14 

44 

45 

42.80 

13.91 

42.74 

14.09 

42.67 

14.28 

42  .  6  1 

14.46 

45 

46 

43.75 

14.21 

43.69 

14.41 

43.62 

14.60 

43.56 

14.79 

46 

47 

44.70 

14.52 

44.64 

14.72 

44.57 

14.91 

44.51 

15.11 

47 

48 

45.65 

14.83 

45  .  59 

15.03 

45.52 

15.23 

45.45 

15.43 

48 

49 

46.60 

15.14 

46.54 

15.:?5 

46.47 

15.55 

46.40 

rs  .  75 

49 

50 

47.55 

15.45 

47.48 

1  5  .  06  ! 

47.42 

15.87 

47.35 

16.07 

50 

e 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

5 

72  Deg. 

7  If  Deg. 

7H  Deg. 

71*  Deg. 

b 

TRA    ERSE    TABLE. 


C 

18  Deg. 

18|  Deg. 

18£  Deg. 

18|  Deg. 

g 

stance. 

stance.! 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

18.50 

15.76 

48.43 

15.97 

48.36 

16.18 

48.29 

16.39 

51 

52 

49.45 

16.07 

49.38 

16.28 

49.31 

16.50 

49.24 

10.71 

52 

53 

50.41 

16.38 

50.33 

16.60 

50.26 

16.82 

50.19 

17.04 

53 

54 

51.36 

16.69 

51,28 

16.91 

51.21 

17.13 

51.13 

17.36 

54 

55 

52.31 

17.00 

52.23 

17.22 

52.16 

17.45 

52.08 

17.68 

55 

56 

53  .  26 

17.30 

53,18 

17.54 

53.11 

17.77 

53.03 

18.00 

56 

57 

54.21 

17.61 

54.13 

17.85 

54.05 

18.09 

53.98 

18.32 

57 

58 

55.16 

17.92 

55.08 

18.16 

55.00 

18.40 

54.92 

18.64 

58 

59 

56  .  1  1 

18.23 

56.03 

18.48 

55.95 

18.72 

55.87 

18.96 

59 

60 

57.06 

18.54 

56.98 

18.79 

56.90 

19.04 

56.82 

19.29 

60 

61 

58.01 

18  85 

57.93 

19.10 

57.85 

19.36 

57.76 

19.61 

61 

62 

58.97 

19.16 

58.88 

19.42 

58.80 

19.67 

58.71 

19.93 

62 

63 

59.92 

19.47 

59,83 

19.73 

59  .  74 

19.99 

59.66 

20.25 

63 

64 

60.87 

19.78 

60.78 

20.04 

60,69 

20.31 

60.60 

20.57 

64 

65 

61.82 

20.09 

61,73 

20.36 

61.64 

20.62 

61.55 

20.89 

65 

66 

62.77 

20.40 

62,68 

20.67 

62,59 

20.94 

62.50 

21.22 

66 

67 

63.72 

20.70 

63,63 

20.98 

63.54 

21.26 

63.44 

21.54 

67 

68 

64.67 

21.D1 

64.58 

21.30 

64,49 

21.58 

64.39 

21.86 

68 

69 

65.62 

21.32 

65.53 

21,61 

65.43 

21,89 

65.34 

22.18 

69 

70 

66.57 

21.63 

66.48 

21.92 

66.38 

22.21 

66.29 

22.50 

70 

71 

67.53 

21.94 

67.43 

22,23 

67,33 

22.53 

67.23 

22.82 

71 

72 

68.48 

22.25 

68.38 

22.55 

68,28 

22.85 

68.18 

23.14 

72 

73 

69.43 

22,56 

69.33 

22.86 

69.23 

23.16 

69.13 

23.47 

73 

74 

70.38 

22,87 

70.28 

23.17 

70.18 

23,48 

70.07 

23.79 

74 

75 

71.33 

23.18 

71.23 

23.49 

71,12 

23.80 

71.02 

24.11 

75 

76 

72  .  28 

23.49 

72.18 

23.80 

72.07 

24.  i2 

71,97 

24.43 

76 

77 

73.23 

23  .  79 

73.13 

24.11 

73.02 

24.43 

72.91 

24.75 

77 

78 

74.18 

24.10 

74.08 

24.43 

73.97 

24,75 

73.86 

25.07 

78 

79 

75.13 

24.41 

75.03 

24.74 

74.92 

25,07 

74.81 

25.39 

79 

80 

76.08 

24  .  72 

75  .  98 

25.05 

75.87 

25.38 

75.75 

25.72 

80 

81 

77.04 

25.03 

76  .  93 

25.37 

76.81 

25  .  70 

76.70 

26.04 

81 

82 

77.99 

25.34 

77.88 

25,68 

77.76 

26.02 

77.65 

26.36 

82 

83 

78  .  94 

25  .  65 

78.83 

25.99 

78.71 

26.34 

78.60 

2«.68 

83 

84 

79.89 

25.96 

79.77 

26.31 

79.66 

26.65 

79.54 

27.00 

84 

85 

80.84 

26.27 

80.72 

26  .  62 

80.61 

26.97 

80.49 

27.32 

85 

86 

81.79 

26.58 

81.67 

26.93 

81.56 

27.29 

81.44 

27.64 

86 

87 

82.74 

26.88 

82.62 

27.25 

82.50 

27.61 

82.38 

27.97 

87 

88 

83.69 

27.19 

83.57 

27.56 

83,45 

27.92 

83.33 

28.29 

88 

89 

84  .  64 

27.50 

84.52 

27.87 

84.40 

28.24 

84.28 

28.61 

89 

90 

85  .  60 

27.81 

85.47 

28.18 

85.35 

28.56 

85.22 

28.93 

90 

91 

§6  .  55 

28.12 

86.42 

28.50 

86.30 

28.37 

86.17 

29.25 

91 

92 

87.50 

28.43 

87.37 

28.81 

87.25 

29.19 

87.12 

29.57 

92 

93 

88.45 

28.74 

88.32 

29.12 

88.19 

29.51 

88.06 

29.89 

93 

94 

89.40 

29.05 

89.27 

29.44 

89.14 

29.83 

89.01 

30.22 

94 

95 

90.35 

29.36 

90.22 

29.75 

90.09 

30.14 

89.96 

30.54 

95 

96 

91.30 

29.67 

91.17 

30.06 

91.04 

30.46 

90.91 

30.86 

96 

97 

92.25 

29.97 

92.12 

30.38 

91.99 

30.78 

91.85 

31.18 

97 

98 

93.20 

30.28 

93.07 

30.69 

92.94 

31.10 

92.80 

31.50 

98 

99 

94.15 

30.59 

94.02 

31.00 

93.88 

31.41 

93.75 

31.82 

99 

100 

95.11 

30.90 

94.97 

31.32 

94.83 

31.73 

94.69 

32.14 

100 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.  |   Lat. 

1 

3 

72  Deg. 

71|  Deg. 

711  Deg. 

714  Deg. 

cd 

Q 

40 


TRAVERSE   TABLE. 


1 

19Deg. 

19*  Deg. 

19*  Deg. 

19|  Deg. 

g 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

1 

0.95 

0.33 

0.94 

0.33 

0.94 

0.33 

0.94 

0.34 

1 

2 

1.89 

0.65 

1.89 

0.66 

1.89 

0.67 

1.88 

0.68 

2 

3 

2.84 

0.98 

2.83 

0.99 

2.83 

1.00 

2.82 

1.01 

3 

4 

3.78 

1.30 

3.78 

1.32 

3.77 

1.34 

3.76 

1.35 

4 

5 

4.73 

1.63 

4.72 

1.65 

4.71 

1.67 

4.71 

1.69 

5 

6 

5.67 

1.95 

5.66 

1.98 

5.66 

2.00 

5.65 

2.03 

6 

7 

6.62 

2.28 

6.61 

2.31 

6.60 

2.34 

6.59 

2.37 

7 

8 

7.56 

2.60 

7.55 

2.64 

7.54 

2.67 

7.53 

2.70 

8 

9 

8.51 

2.93 

8.50 

2.97 

8.48 

3.00 

8.47 

3.04 

9 

10 

9.46 

3.26 

9.44 

3.30 

9.43 

3.34 

9.41 

3.38 

10 

11 

10.40 

3.58 

10.38 

3.63 

10.37 

3.67 

10.35 

3.72 

11 

12 

11.35 

3.91 

11.33 

3.96 

11.31 

4.01 

11.29 

4.06 

12 

13 

12.29 

4.23 

12.27 

4.29 

12.25 

4.34 

12.24 

4.39 

13 

14 

13.24 

4.56 

13.22 

4.62 

13.20 

4.67 

13.18 

4.73 

14 

15 

14.18 

4.88 

14.16 

4.95 

14.14 

5.01 

14.12 

5.07 

15 

16 

15.13 

5.21 

15.11 

5.28 

15.08 

5.34 

15.06 

5.41 

16 

17 

16.07 

5.53 

16.05 

5.60 

16.02 

5.67 

16.00 

5.74 

17 

18 

17.02 

5.86 

16.99 

5.93 

16.97 

6.01 

16.94 

6.08 

18 

19 

17.96 

6.19 

17.94 

6.26 

17.91 

6.34 

17.88 

6.42 

19 

20 

18.91 

6.51 

18.88 

6.59 

18.85 

6.68 

18.82 

6.76 

20 

21 

19.86 

6.84 

19.83 

6.92 

19.80 

7.01 

79V76~ 

7.10 

21 

22 

20.80 

7.16 

20  .  77 

7.25 

20.74 

7.34 

20.71 

7.43 

22 

23 

21.75 

7.49 

21.71 

7.58 

21.68 

7.68 

21.65 

7.77 

23 

24 

22.69 

7.81 

22.66 

7.91 

22.62 

8.01 

22.59 

8.11 

24 

25 

23.64 

8.14 

23.60 

8.24 

23.57 

8.35 

23.53 

8.45 

25 

26 

24.58 

8.46 

24.55 

8.57 

24.51 

8.68 

24.47 

8.79 

26 

27 

25.53 

8.79 

25.49 

8.90 

25.45 

9.01 

25.41 

9.12 

27 

28 

26.47 

9.12 

26.43 

9.23 

26.39 

9.35 

26.35 

9.46 

28 

29 

27.42 

9.44 

27.38 

9.56 

27.34 

9.68 

27.29 

9.80 

29 

30 

28.37 

9.77 

28.32 

9.89 

28.28 

10.01 

28.24 

10.14 

30 

31 

29.31 

10.09 

29.27 

10.22 

29.22 

10.35 

29.18 

10.48 

31 

32 

30.26 

10.42 

30.21 

10.55 

30.16 

10.68 

30.12 

10.81 

32 

33 

31.20 

10.74 

31.15 

10.88 

31.11 

11.02 

31.06 

11.15 

33 

34 

32.15 

11.07 

32.10 

11.21 

32.05 

11.35 

32.00 

11.49 

34 

35 

33.09 

11.39 

33.04 

11.54 

32  .  99 

11.68 

32.94 

11.83 

85 

36 

34.04 

1  1  .  72 

33.99 

11.87 

33.94 

12.02 

33.88 

12.17 

36 

37 

34.98 

12.05 

34.93 

12.20 

34.88 

12.35 

34.82 

12.50 

37 

38 

35.93 

12.37 

35.88 

12.53 

35.82 

12.68 

35  .  76 

12.84 

38 

39 

36.88 

12.70 

36.82 

12.86 

36.70 

13.02 

36.71 

13.18 

39 

40 

37.82 

13.02 

37.76 

13.19 

37.71 

13.35 

37.65 

13.52 

40 

41 

38.77 

13.35 

38.71 

13.52 

38  .  65 

13.69" 

38.59 

13.85 

41 

42 

39.71 

13.67 

39.65 

13.85 

39.59 

14.02 

39.53 

14.19 

42 

43 

40.66 

14.00 

40.60 

14.18 

40.53 

14.35 

40.47 

14.53 

43 

44 

41.60 

14.32 

41.54 

14.51 

41.48 

14.69 

41.41 

14.87 

44 

45 

42.55 

14.65 

42.48 

14.84 

42.42 

15.02 

42.35 

15.21 

45 

46 

43.49 

14.98 

43.43 

15.17 

43.36 

15.36 

43.29 

15.54 

46 

47 

44.44 

15.30 

44.37 

15.50 

44.30 

15.69 

44.24 

15.88 

47 

48 

45.38 

15.63 

45.32 

15.83 

45.25 

16.02 

45.18 

16.22 

48 

49 

46.33 

15.95 

46.26 

16.15 

46.19 

16.  56 

46.12 

16.56 

49 

50 

47.28 

16.28 

47.20 

16.48 

47.13 

16.69 

47,06 

16.90 

50 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lai. 

o 

o 
0 

.2 

Q 

71  Deg. 

70£  Deg. 

70  &  Deg. 

70}  Deg. 

s 

TH AVERSE   TABLE. 


41 


g 

19  Deg. 

191  Deg. 

19£  Dog. 

19|  Deg. 

g 

00 

I 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p 

51 

48.22 

16.60 

48.15 

16.81 

48.07 

17.02 

48.00 

17.23 

51 

52 

49.17 

16.93 

49.09 

17.14 

49.02 

17.36 

48.94 

17.57 

52 

53 

50.11 

17.26 

50.04 

17.47 

49.96 

17.69 

49.88 

17.91 

53 

54 

51.06 

17.58 

50.98 

17.80 

50.90 

18.03 

50.82 

18.25 

54 

55 

52.00 

17.91 

51.92 

18.13 

51.85 

18.36 

51.76 

18.59 

55 

56 

52.95 

18.23 

52.87 

18.46 

52.79 

18.69 

52.71 

18.92 

56 

57 

53.89 

18.56 

53.81 

18.7-9 

53.73 

19.03 

53.65 

19.26 

57 

58 

54.84 

18.88 

54.76 

19.12 

54.67 

19.36 

54.59 

19.60 

58 

59 

55.79 

19.21 

55.70 

19.45 

55.62 

19.69 

55.53 

19.94 

59 

60 

56.73 

19.53 

56.65 

19.78 

58.56 

20.03 

56.47 

20.27 

60 

61 

5^.68 

19.86 

57.59 

20.11 

57.50 

20.36 

57.41 

20.61 

61 

62 

58.62 

20.19 

58.53 

20.44 

58.44 

20.70 

58.35 

20,95 

62 

63 

59.57 

20.51 

59.48 

20.77 

59.39 

21.03 

59.29 

21.29 

63 

64 

60.51 

20.84 

60.42 

21.10 

60.33 

21.36 

60.24 

21.63 

64 

65 

61.46 

21.16 

61.37 

21.43 

61.27 

21.70 

61.18 

21.96 

65 

66 

62.40 

21.49 

62.31 

21.76 

62.21 

22.03 

62.12 

22.30 

66 

67 

63.35 

21.81 

63.25 

22.09 

63.16 

22.37 

63.06 

22  .  64 

67 

68 

64.30 

22.14 

64.20 

22.42 

64.10 

22.70 

64.00 

22  .  98 

68 

69 

65.24 

22.46 

65.14 

22.75 

65.04 

23.03 

64.94 

23.32 

69 

70 

66.19 

22.79 

66.09 

23.08 

65.98 

23.37 

65.88 

23  .  65 

70 

71 

67.13 

23.12 

67.03 

23.41 

66.93 

23.70 

66.82 

23.99 

71 

72 

68.08 

23.44 

67.97 

23.74 

67.87 

24.03 

67.76 

24.33 

72 

73 

69.02 

23  .  77 

68.92 

24.07 

68.81 

24.37 

68.71 

24.67 

73 

74 

69.97 

24.09 

69.86 

24.40 

69.76 

24.70 

69  .  65 

25.01 

74 

75 

70.91 

24.42 

70.81 

24  .  73 

70.70 

2C.04 

70  .  59 

25.34 

75 

76 

71.86 

24.74 

7  1  .  75 

25.06 

71.64 

25.37 

71.53 

25  .  68 

76 

77 

72.80 

25.07 

72.69 

25.39 

72.58 

25.70 

72.47 

26.02 

77 

78 

73.75 

25  .  39 

73.64 

25.72 

73.53 

26.04 

73.41 

26.36 

78 

79 

74.70 

25.72 

74.58 

26.05 

74.47 

26.37 

74.35 

26.70 

79 

80 

75.64 

26.05 

75.53 

26.38 

75.41 

26.70 

75.29 

27.03 

80 

81 

76.59 

26.37 

76.47 

26.70 

76.35 

27.04 

76.24 

27.37 

81 

82 

77.53 

26.70 

77.42 

27.03 

77.30 

27.37 

77.18 

27.71 

82 

83 

78.48 

27.02 

78.36 

27.36 

78.24 

27.71 

78.12 

28.05 

83 

84 

79.42 

27.35 

79.30 

27.69 

79.18 

28.04 

79.06 

28.39 

84 

85 

80.37 

27.67 

80  .  25 

28.02 

80.12 

28.37 

80.00 

28  .  72 

85 

86 

81.31 

28.00 

81.19 

28.35 

81.07 

28.71 

80.94 

29.06 

86 

87 

82.26 

28.32 

82.14 

28.68 

82.01 

29.04 

81.88 

29.40 

87 

88 

83.21 

28  .  65 

83.08 

29.01 

92.95 

29.37 

82.82 

29.74 

88 

89 

84.15 

28.98 

84.02 

29.34 

83.90 

29.71 

83.76 

30.07 

89 

90 

85.10 

29.30 

84.97 

29.67 

84.84 

30.04 

84.71 

30.41 

90 

91 

86.04 

29.63 

85.91 

30.00 

85.78 

30.38 

85.65 

30.75 

91 

92 

86.99 

29.95 

86.86 

30.33 

86.72 

30.71 

86.59 

31.09 

92 

93 

87.93 

30.28 

87.80 

30.66 

87.67 

31.04 

87.53 

31  .43 

93 

94 

88.88 

30.60 

88.74 

30.99 

88.61 

31.38 

8-8.47 

31.76 

94 

95 

89.82 

30.93 

89.69 

31.32 

89.55 

31.71 

89.41 

32.10 

95 

96 

90.77 

31.25 

90.63 

31.65 

90.49 

32.05 

90.35 

32.44 

96 

97 

91.72 

31.58 

91.58 

31.98 

91.44 

32.38 

91.29 

32.78 

97 

98 

92.66 

31.91 

92.52 

32.31 

92.38 

32.71 

92.24 

33.12 

98 

99 

93.61 

32.23 

93.46 

32.64 

93.32 

33.05 

93.18 

33.45 

99 

100 

94.55 

32.56 

94.41 

32.97 

94.26 

33.38 

94.12 

33.79 

100 

I 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<v 
u 

3 

-2 

OB 

3 

71  Deg. 

70|  Deg. 

70|  Deg. 

70J  Deg. 

01 

5 

TRAVERSE    TABLE. 


Distance.! 

20  Deg. 

20i  Deg. 

2QJ  Deg. 

20J  Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Let. 

Dep. 

1 

0.94 

0.34 

0.94 

0.35 

0.94 

0.35 

0.94 

0.35 

1 

2 

1.88 

0.68 

1.88 

0.69 

1.87 

0.70 

1.87 

0.71 

2 

3 

2.82 

1.03 

2.81 

1.04 

2.81 

1.05 

2.81 

1.06 

3 

4 

3.76 

1.37 

3.75 

1.38 

3.75 

1.40 

3.74 

1.42 

4 

5 

4.70 

1.71 

4.69 

1.73 

4.68 

1.75 

4.68 

1.77 

5 

6 

5.64 

2.05 

5.63 

2.08 

5.62 

2.10 

5.61 

2.13 

6 

7 

6.58 

2.39 

6.57 

2.42 

6.56 

2.45 

6.55 

2.48 

7 

8 

7.52 

2.74 

7.51 

2.77 

7.49 

2.80 

7.48 

2.83 

8 

9 

8.46 

3.08 

8.44 

3.12 

8.43 

3.15 

8.42 

3.19 

9 

10 

9.  '40 

3.42 

9.38 

3.46 

9.37 

3.50 

9.35 

3.54 

10 

11 

10.34 

3.76 

10.32 

3.81 

10.30 

3.85 

10.29 

3.90 

11 

12 

11.28 

4.10 

11.26 

4.15 

11.24 

4.20 

11.22 

4.25 

12 

13  12.22 

4.45 

12.20 

4.50 

12.18 

4.55 

12.16 

4.61 

13 

14 

13.16 

4.79 

13.13 

4.85 

13.11 

4.90 

13.09 

4.96 

14 

15 

14.10 

5.13 

14.07 

5.19 

14.05 

5.25 

14.03 

5.31 

15 

16 

15.04 

5.47 

15.01 

5.54 

14.99 

5.60 

14.96 

5.67 

16 

17 

15.97 

5.81 

15.95 

5.88 

15.92 

5  .  95 

15.90 

6.02 

17 

18 

16.91 

6.16 

16.89 

6.23 

16.86 

6.30 

16.83 

6.38 

18 

19 

17.85 

6.50 

17.83 

6.58 

17.80 

6.65 

17.77 

6.73 

19 

20 

18.79 

6.84 

18.76 

6.92 

18.73 

7.00 

18.70" 

7.09 

20 

21 

19.73 

7.18 

19.70 

7.27 

19.67 

7.35 

19.64 

7.44 

21 

22 

20  .  67 

7.52 

20.64 

7.61 

20.61 

7.70 

20.57 

7.79 

22 

23 

21.  Cl 

7.87 

21.58 

7.96 

21.54 

8.05 

21.51 

8.15 

23 

24 

22  .  55 

8.21 

22.52 

8.31 

22.48 

8.40 

22.44 

8.50 

24 

25 

23.49 

8.55 

23.45 

8.65 

23.42 

8.76 

23.38 

8.86 

25 

26 

24.43 

8.89 

24.39 

9.00 

24.35 

9.11 

24.31 

9.21 

26 

27 

25.37 

9.23 

25.33 

9.35 

25  .  29 

9.46 

25.25 

9  .  57 

27 

28 

26.31 

9.58 

26.27 

9.69 

26.23 

9.81 

26.18 

9.92 

28 

29 

27.25 

9.92 

27.21 

10.04 

27.16 

10.16 

27.12 

10.27"- 

29 

30 

28.19  10.26 

28.15 

10.38 

28.10 

10.51 

28  .  05 

10.63 

30 

31 

29.13 

10.60 

29  .  08 

10.73 

29.04 

10.86 

28.99 

10.98 

31 

32 

30.07 

10.94 

30.02 

11.08 

29.97 

11.21 

29.92 

11.34 

32 

33 

31.01 

11.29 

30.96 

11.42 

30.91 

11.56 

30.88 

11.69 

33 

34 

31.95 

11.63 

31.90 

11.77 

31.85 

11.91 

31.79 

12.  On 

34 

35 

32.89 

11.97 

32.84 

12.11 

32.78 

12.26 

32.73 

12.40 

35 

36 

33.83 

12.31 

33.77 

12.46 

33  .  72 

12.61 

33.66 

12.75 

36 

37 

34.77 

12.65 

34.71 

12.81 

34  .  66 

12.96 

34.60 

13.11 

37 

38 

35.71 

13.00 

35.65 

13.15 

35  .  59 

13.31 

35  .-54 

13.46 

38 

39 

36  .  65 

13.34 

36.59 

13.50 

36  .  53 

13.66 

36.47 

13.82 

39 

40 

37.59!  13.68 

37  .  53 

13.84 

37.47 

14.01 

37.41 

14.17 

40 

41 

38.53 

14.02 

38.47 

14.19 

38.40 

14.36 

38.34 

14.53 

41 

42 

39.47 

14.36 

39.40 

14.54 

39.34 

14.71 

39.28 

14.88 

42 

43 

40.41 

14.71 

40.34 

14.88 

40.28 

15.06 

40.21 

15.23 

43 

44 

41.35  15.05 

41.28 

15.23 

41.21 

15.41 

41.15 

15.59 

44 

45 

42  .  29 

15.39 

42  .  22 

15.58 

42.15 

15.76 

42.08 

15.94 

45 

46 

43.23 

15.73 

43.16 

15.92 

43.09 

16.11 

43.02 

16.30 

46 

47 

44.17 

16.07 

44.09 

16.27 

44.02 

16.46 

43.95 

16.65 

47 

48 

45.11 

16.42 

45.03 

16.61 

44.96 

16.81 

44.89 

17.01 

48 

49 

46.04 

16.76 

45.97 

16.96 

45.90 

17.16 

45.82 

17.36 

49 

50 

46,98 

17.10 

46.91 

17.31 

46.83 

17.51 

46.715 

17.71 

50 

Q 
o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

c3 

1 

Q 

70  Deg. 

69|  Deg. 

69i  Deg. 

69i  Deg. 

Q 

TRAVERSE    TABLE. 


43 


3T 

20  Deg. 

20i  Deg. 

20£  Deg. 

20f  Deg. 

ft 

Q9 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.  1 

Dep. 

Lat. 

Dep. 

3 
O 
CD 

51 

47.92 

17.44  | 

i~.35 

17.65 

47.77 

17.86  ! 

47.69 

18.07 

51 

52 

48.86 

17.79 

48.79 

18.00 

48.71 

18.21 

48.63 

18.42 

52 

53 

49.80 

18.13 

49.72 

18.34 

49.64 

18.56 

49.56 

18.78 

53 

54 

50.74 

18.47 

50.66 

18.69 

50.58 

18.91 

50  .  50 

19.13 

54 

55 

51.63 

18.81 

51.60 

19.04 

51.52 

19.26 

51.43 

19.49 

55 

56 

52.62 

19.15 

52.54 

19.38 

52.45 

19.61 

52.37 

19.84 

56 

57 

53.56 

19.50 

53.48 

19.73 

53.39 

19.96 

53.30 

20.19 

57 

58 

54.50 

19.84 

54.42 

20.07 

54.33 

20.31  1 

54.24 

20.55 

58 

59 

55.44 

20.18 

55.35 

20.42 

55.26 

20.661 

55.17 

20.90 

59 

60 

56.33 

20.52 

56.29 

20.77 

56.20 

21.01 

56  .  1  1 

2  1  .  26 

60 

61 

57.32 

20.86 

57.23 

21.11 

57.14 

21.36 

57.04 

21.61 

61 

62 

58.26 

21.21 

58.17 

21.46 

58.07 

21.71 

57.98 

21.97 

62 

63 

59.20 

21.55 

59.11 

21.81 

59.01 

22.06 

58.91 

22.32 

63 

64 

60.14 

21.89 

60.04 

22.15 

59  .  95 

22.41 

59.85 

22  .  67 

64 

65 

61.08 

22.23 

60.93 

22.50 

60.83 

22.76 

60.78 

23.03 

65 

66 

62  .  02 

22  .  57 

61.92 

22  .  84 

61.82 

23.11 

61.72 

23  .  38 

66 

67 

62.96 

22.92 

62.86 

23.19 

62.76 

23.46! 

62.65 

23  .  74 

67 

68 

63.90 

23.26 

63.80 

23.54 

63.69 

23.81 

63.59 

24.09 

68 

69 

64.84 

23.60 

64.74 

23.88 

64.63 

24.16 

64.52 

24.45 

69 

70 

65.78 

23.94 

65.67 

24.23 

65.57 

24.51  i 

65.46 

24.80 

70 

71 

66  .  72 

24.28 

66.61 

24.57 

66.50 

24.86 

66.39 

25.15 

71 

72 

67.66 

24.63 

67.55 

24.92 

67.44 

25.21 

67.33 

25.51 

72 

73 

68.60 

24.97 

68.49 

25.27 

68.33 

25.57 

68.26 

25.86 

73 

74 

69.54 

25.31 

69.43 

25.61 

69.31 

25.92 

•69.20 

26.22 

74 

75 

70.48 

25.65  1  70.36 

25.96 

70.25 

26.27 

70.14 

26.57 

75 

76 

71.42 

25.99 

71.30 

26.30 

71.19 

26.62 

71.07 

26.93 

76 

77 

72.36 

26.34 

72.24 

26.65 

72.12 

26.97 

72.01 

27.28 

77 

78 

73.30 

26.68 

73.18 

27.00 

73.06 

27.32 

72  .  94 

27.63 

78 

79 

74.24 

27.02 

74.12 

27.34 

74.00 

27  .  67 

73.88 

27.99 

79 

80 

75.18 

27.36 

75.06 

27.69 

74.93 

23.02 

74.81 

28.34 

80 

81 

76.12 

27.70 

75.99 

28.04 

75.87 

28.37 

75  .  75 

28  .  70 

81 

82 

77.05 

28.05 

76  .  93 

23.33 

76.81 

28  .  72 

76.68 

29.05 

82 

83 

77.99 

28.39 

77.87 

28  .  73 

77.74 

29.07 

77.62 

29.41 

83 

84 

78.93 

28.73 

78.81 

29.07 

78.68 

29.42 

78  .  55 

29.76 

84 

85 

79.87 

29.07 

79  .  75 

29.42 

79.62 

29.77 

79.49 

30.11 

85 

86 

80.81 

29.41 

80.68 

29.77 

80  .  55 

30.12 

80.42 

30.47 

86 

87 

81.75 

29^76 

81.62 

30.11 

81.49 

30.47 

81.36 

30.82 

87 

88 

82.69 

30.10 

82.56 

30.46 

82.43 

30  .  82 

82.29 

31.18 

83 

89 

83.63 

30.44 

83.50 

30.80 

83.36 

31.17 

83.23 

3  1  .  53 

89 

90 

84.57 

30.78 

84.44 

31.15 

84.30 

31.52 

84  .  1  o 

31.89 

90 

91 

85.51 

31.12 

85.38 

31.50 

85.24 

31.87 

85.10 

32.24 

91 

92 

86.45 

31.47 

86.31 

31.84 

86.17 

32.22 

86.03 

32.59 

92 

93 

87.39 

31.81 

87.25 

32.19 

87.11 

32.57 

86.97 

32.93 

93 

94 

88.33 

32.15 

88.19 

32  .  54 

88.05 

32.92 

87.90 

33.30 

94 

95 

89.27 

32.49 

89.13 

32.88 

,83.93 

33.27 

88.84 

33.66 

95 

96 

90.21 

32.83 

90.07 

33.23 

89.92 

33.62 

89.77 

34.01 

96 

97 

91.15 

33.18 

91.00 

33.57 

90.86 

33.97 

90.71 

34.37 

97 

98 

92.09 

33.52 

91.94 

33.92 

91.79 

34.32 

91.64 

34  .  72 

93 

99 

93.03 

33.86 

92.88 

34.27 

92.73 

34.67 

92.58 

35.07 

99 

100 

93.97 

34.20 

93.82 

34.61 

93.67 

35.02 

93.51 

35.43 

100 

8 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

.5 

Q 

70  Deg. 

69|  Deg. 

69|  Deg. 

694  l>eg 

Q 

44 


TRAVERSE    TABLE. 


o 

..  •  •  *•>-•*•  **•  .•  ' 
21  Deg. 

2U  Deg. 

II 
21|  Deg.             21|  Deg. 

C 

33° 

55° 

p 

Dep. 

Lat. 

j 

fa 
P 

Lat. 

Lat. 

Dep. 

Dep. 

Lat. 

Dep. 

1 

0.93 

0.36 

0.93 

0.36 

0.93 

O.oTI 

0.93 

0.37 

1 

2 

1.87 

0.72 

1.86 

0.72 

1.86 

0.73 

1.86 

0.74 

2 

3 

2.80 

1.08 

2.80 

1.09 

2.79 

1.10 

2.79 

1.11 

3 

4 

3.73 

1.43 

3.73 

1.45 

3.72 

1.47 

3.72 

1.48 

.4 

5 

4.67 

1.79 

4.66 

1.81 

4.65 

1.83 

4.64 

1.85 

5 

6 

5.60 

2.15 

5.59 

2.17 

5.58 

2.20 

5.57 

2.22 

6 

7 

6.54 

2.51 

6.52 

2.54 

6.51 

2.57 

6.50 

2.59 

7 

8 

7.47 

2.87 

7.46 

2.90 

7.44 

2.93 

7.43 

2.96 

8 

9 

8.40 

3.23 

8.39 

3.26 

8.37 

3.30 

8.36 

3.34 

9 

10 

9.34 

3.58 

9.32 

3.62 

9.30 

3.67 

9.29 

3.71 

10 

11 

10.27 

3.94 

10.25 

3.99 

10.23 

4.03 

10.22 

4.08 

11 

12 

11.20 

4.30 

11.18 

4.35 

11.17 

4.40 

11.15 

4.45 

12 

13 

12.14 

4.66 

12.12 

4.71 

12.10 

4.76 

12.07 

4.82 

13 

14 

13.07 

5.02 

13.05 

5.07 

13.03 

5.13 

13.00 

5.19 

14 

15 

14.00 

5.38 

13.98 

5.44 

13.96 

5.50 

13.93 

5.56 

15 

16 

14.94 

5.73 

14.91 

5.80 

14.89 

5.86 

14.86 

5.93 

16 

17 

15.87 

6.09 

15.84 

6.16 

15.82 

6.23 

15.79 

6.30 

17 

18 

16.80 

6.45 

16.78 

6.52 

16.75 

6.60 

16.72 

6.67 

18 

19 

17.74 

6.81 

IT".  71 

6.89 

17.68 

6.96 

17.65 

7.04 

19 

20 

18.67 

7.17 

18.64 

7.25 

18.61 

7.33 

18.58 

7.41 

20 

21 

19.61 

7.53 

19.57 

7.61 

19.54 

7.70 

19.50 

7.78 

21 

22 

20.54 

7.88 

20.50 

7.97 

20.47 

8.06 

20.43 

8.15 

22 

23 

21.47 

8.24 

21.44 

8.34 

21.40 

8.43 

21.36 

8.52 

23 

24 

22.41 

8.60 

22.37 

8.70 

22.33 

8.80 

22.29 

8.89 

24 

25 

23.34 

8.96 

23.30 

9.06 

23.26 

9.16 

23.22 

9.26 

25 

26 

24.27 

9.32 

24.23 

9.42 

24.19 

9.53 

24.15 

9.63 

26 

27 

25.21 

9.68 

25.16 

9.79 

25.12 

9.90 

25.08 

10.01 

27 

28 

26.14 

10.03 

26.10 

10.15 

26.05 

10.26 

26.01 

10.38 

28 

29 

27.07 

10.39 

27.03 

10.51 

26.98 

10.63 

26.94 

10.75 

29 

30 

28.01 

10.75 

27.96 

10.87 

27.91 

11.00 

27.86 

11.12 

30 

31 

28.94 

11.11 

28.89 

11.24 

28.84 

11.36 

28  .  79 

11.49 

31 

32 

29.87 

11.47 

29.82 

11.60 

29.77 

11.73 

29  .  72 

11.86 

32 

33 

30.81 

11.83 

30.76 

11.96 

30.70 

12.09 

30.65 

12.23 

33 

34 

31.74 

12.18 

31.69 

12.32 

31.63 

12.46 

31.58 

12.60 

34 

35 

32.68 

12.54 

32.62 

12.69 

32  .  56 

12.83 

32.51 

12.97 

35 

36 

33.61 

12.90 

33.55 

13.05 

33.50 

13.19 

33.44 

13.34 

36 

37 

34.54 

13.26 

34.48 

13.41 

34.43 

13.56 

34.37 

13.71 

37 

38 

35.48 

13.62 

35.42 

13.77 

35.36 

13.93 

35.29 

14.08 

38 

39 

36.41 

13.98 

36.35 

14.14 

36.29 

14.29 

36.22 

14.45 

39 

40 

37.34 

14.33 

37.28 

14.50 

37.22 

14.66 

37.15 

14.82 

40 

41 

33.28 

14.69 

38.21 

14.86 

38.15 

15.03 

38.08 

15.19 

41 

42 

39.21 

15.05 

39.14 

15.22 

39.08 

15.39 

39.01 

15.56 

42 

43 

40.14 

15.41 

40.08 

15.58 

40.01 

15.76 

39.94 

15.93 

43 

44 

41.08 

15,77 

41.01 

15.95 

40.94 

16.13 

40.87 

16.30 

44 

45 

42.01 

16.13 

41.94 

16.  3.1 

41.87 

16.49 

41.80 

16.68 

45 

46 

42.94 

16.48 

42.87 

16.67 

42.80 

16.86 

42.73 

17.05 

46 

47 

43.88 

16.84 

43.80 

17.03 

43.73 

17.23 

43.65 

17.42 

47 

48 

44.81 

17.20 

44.74 

17.40 

44.66 

17.59 

44.58 

17.79 

48 

49 

45  .  75 

17.56 

45.67 

17.76 

45.59 

17.96 

45.51 

18.16 

49 

BO 

46.68 

17.92 

46.60 

18.12 

46.52 

18.33 

46.44 

18.53 

50 

'i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

£ 

1 

Q  1       69  Deg. 

68|  Deg. 

681  Deg. 

68|  Deg. 

Q 

TRAVERSE    TABLE. 


45 


« 

21  Deg. 

2H  Deg. 

21£  Deg. 

21  1  Deg. 

O 

55' 

OT* 

P 

3 

3 
o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 
?. 

51 

47.61 

18.28 

47.53 

18.48 

47.45 

18.69 

47.37 

18.90 

TjJ 

52 

48.55 

18.64 

48.46 

18.85 

48.38 

i9.ee 

48.30 

19.27 

52 

53 

49.48 

18.99 

49.40 

19,21 

49.31 

19.42 

49  .  23 

19.64 

53 

54 

50.41 

19.35 

50.33 

19.57 

50.24 

19.79 

50.16 

20.01 

54 

55 

51.35 

19.71 

51.26 

19.93 

51.17 

20.16 

51.08 

20.38 

55 

56 

52  28 

20.07 

52.19 

20  .  3.0 

52.10 

20  .  52 

52.01 

20.75 

56 

57 

53  21 

20.43 

53.12 

20  .  66 

53.03 

20.89 

52.94 

21.12 

57 

58 

54.15 

20  .  79 

54.06 

21.02 

53.96 

21.26 

53.87 

21.49 

58 

59 

55.08 

21.14 

54.99 

21.38 

54.89 

21.62 

54.80 

21.86 

59 

60 

56.01 

21.50 

55.92 

21.75 

55.83 

21.99 

55.73 

22.23 

60 

61 

56  .  95 

21.86 

56.85 

22  .  1  1 

56.76 

22  .  36 

56  .  66 

22,60 

61 

62 

57.88 

22  22 

57.78 

22.47 

57.69 

22.72 

57.59 

22.97 

62 

63 

58.82 

22!  58 

58,72 

22.83 

58.62 

23.09 

58.52 

23.35 

63 

64 

59.75 

22.94 

59  .  65 

23.20 

59  .  55 

23.46 

59.44 

23  .  72 

64 

65 

60.68 

23.29 

60.58 

23.56 

60.48 

23.82 

60.37 

24.09 

65 

66 

61.62 

23.65 

61.51 

23.92 

61.41 

24.19 

61.30 

24.46 

66 

67 

62  .  55 

24.01 

62.44 

24.28 

62.34 

24.56 

62.23 

24.83 

67 

68 

63.48 

24.37 

63.38 

24.65 

63.27 

24.92 

63.16 

25.20 

68 

69 

64.42 

24.73 

64.31 

25.01 

64.20 

25.29 

64.09 

25.57 

69 

70 

65.35 

25.09 

65.24 

25.37 

65.13 

25.66 

65.02 

25  .  94 

70 

"71 

6h.28. 

25.44J 

66.17 

25.73 

66.06 

26.02 

65  .  95 

26.31 

71 

72 

67.22 

25.80 

67.10 

26.10 

66.99 

26.39 

66.87 

26.68 

72 

73 

68.15 

26.16 

68  .  04 

26.46 

67.92 

26  .  75 

67.80 

27.05 

73 

74 

69.08 

26.52 

68.97 

26.82 

68.85 

27.12 

68.73 

27.42 

74 

75 

70.02 

26.88 

69.90 

27.18 

69.78 

27.49 

69  .  66 

27.79 

75 

76 

70.95 

27.24 

70.83 

27.55 

70.71 

27.85 

70.59 

28.16 

76 

77 

71.89 

27.59 

71.76 

27.91 

71.64 

28.22 

71.52 

28.53 

77 

78 

72.82 

27.95 

72.70 

28.27 

72.57 

28.59 

72.45 

28.90 

78 

79 

73  .  75 

28.31 

73.63 

28  .  63 

73.50 

28.95 

73.38 

29.27 

79 

80 

74.69 

28.67 

74.56 

29.00 

74.43 

29.32 

74.30 

29.64 

80 

81 

75.62 

29.03 

75.49 

29  .  38 

75.36 

29.69 

75.23 

30.02 

81 

82 

76  .  55 

29.39 

76.42 

29.72 

76.29 

30.05 

76  .  16 

30.39 

82 

83 

77.49 

29.74 

77.36 

30.08 

77  .  22 

30.42 

77.09 

30.76 

83 

84 

78.42 

30.10 

78.29 

30.44 

78.16 

30.79 

78.02 

31.13 

84 

85 

79.35 

30.46 

79.22 

30.81 

i  79.09 

31.15 

78  .  95 

31.50 

85 

86 

80.29 

30.82 

80.15 

31.  11*  ^80.02 

31.52 

79  .  88 

31.87 

86 

87 

81.22 

31.18 

81.08 

31.53 

80  .  95 

31.89 

80.81 

32.24 

87 

88 

82.16 

31.54 

82.02 

31.89 

81.88 

32.25 

81.74 

32.61 

88 

89 

83.09 

31.89 

82.95 

32.26 

82.81 

32  .  62 

82.66 

32.98 

39 

90 

84.02 

32.25 

83.88 

32  .  62  !  83  .  74 

32.99 

83.59 

33  .  35 

90 

91 

84.96 

32.61 

!  84.81 

32.98  |  84.67 

33.35 

184.52 

33  .  72 

91 

92 

85.89 

32.97 

85  .  74 

33.34  i!  85.60 

33.72 

85.45 

34.09 

92 

93 

86.82 

33  .  33 

86.68 

33.71  •  86.53 

34.08 

86.38 

34.46 

93 

94 

87.76 

33.89 

87.61 

34.07  !  87.46 

34.45 

87.31 

34.83 

94 

95 

8S.69 

34.04 

88.54 

34.43  ij  88.39 

34.82 

88.24 

35.20 

95 

96 

89.62 

34.40 

89.47 

34.79  89.32 

35.18 

89.17 

35.57 

96 

97 

90.56 

34.76 

90.40 

35".  16  i  90.25 

35.55 

!  90.09 

35.94 

97 

98 

91.49 

35.12 

91.34 

35*.  52  i  91.18 

35..  92 

91.02 

36.31 

98 

99 

92.42 

35.48 

92.27 

35.88  :j  92.11 

36.28 

91.95 

36  .  69 

99 

100 

93.36 

35.84 

93.20 

36.24  S  98.04 

36.65 

92.88 

37.06 

100 

8 

5 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

rt 

Q 

69  Deg. 

68|  Deg. 

68£  Deg.     68*  Deg. 

Q 

TRAVERSE    TABLE, 


d 

55" 

pT 

22  Deg. 

22*  Deg. 

221  Deg. 

22J  Deg. 

d 
sr 

ID 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

T 

0.93 

0.37 

0.93 

0.38 

0.92 

0  .  33 

0.92 

0.39 

i 

2 

1.85 

0.75 

1.85 

0.76 

1.85 

0.77 

1.84 

0.77 

2 

3 

2.73 

1.12 

2.78 

1.14 

2.77 

1.15 

2.77 

1.16 

3 

4 

3.71 

1.50 

3.70 

1.51 

3.70 

1.53 

3.69 

1.55 

4 

5 

4.64 

1.87 

4.63 

1.89 

4.62 

1.91 

4.61 

1.93 

5 

6 

5.56 

2.25 

5.55 

2.27 

5.54 

2.30 

5.53 

2.32 

6 

7 

6.49 

2.62 

6.48 

2.65 

6.47 

2.68 

6.46 

2.71 

7 

8 

7.42 

3.00 

7.40 

3.03 

7.39 

3.06 

7.38 

3.09 

8 

9 

8.34 

3.37 

8.33 

3.41 

8.31 

3.44 

8.30 

3.48 

9 

10 

9.27 

3  .  75 

9.26 

3.79 

9.24 

3.83 

9.22 

3.87 

10 

11 

10.20 

4.13 

10.18 

4.17 

10.16 

4.21 

10.14 

4.25 

11 

12 

11.13 

4.50 

11.11 

4.54 

11.09 

4.59 

11.07 

4.64 

12 

13 

12.05 

4.87 

12.03 

4.92 

12.01 

4.97 

11.99 

5.03 

13 

14 

12.98 

5.24 

12.96 

5.30 

12.93 

5.36 

12.91 

5.41 

14 

15 

13.91 

5.62 

13.88 

5.68 

13.86 

5.74 

13.83 

5.80 

15 

16 

14.83 

5.99 

14.81 

6.06 

14.78 

6.12 

14.76 

6.19 

16 

17 

15.76 

6.37 

15.73 

6.44 

15.71 

6.51 

15.68 

6.57 

17 

18 

16.69 

6.74 

16.66 

6.82 

16.63 

6.89 

16.60 

6.96 

18 

19 

17.62 

7.12 

17.59 

7.19 

17.55 

7.27 

17.52 

7.3* 

19 

20 

18.54 

7.49 

18.51 

7.57 

18.48 

7.65 

18.44 

7.73 

20 

21 

19.47 

7.87 

19.44 

7.95 

19.40 

8.04 

19.37 

8.12 

21 

22 

20.40 

8.24 

20  .  36 

8.33 

20.33 

8.42 

20.29 

8.51 

22 

23 

21.33 

8.62 

21.29 

8.71  |  21.25 

8.80 

21.21 

8.89 

23 

24 

22.25 

8.99 

22.21 

9.09     22.17 

9.18 

22.13 

9.28 

24 

25 

23.18 

9.37 

23.14 

9.47 

23.10 

9.57 

'23.05 

9.67 

25 

26 

24.11 

9.74 

24.06 

9.84 

24.02 

9.95 

:23.98 

10.05 

26 

27 

25.03 

10.11 

24.99 

10.22 

24.94 

10.33 

124.90 

10.44 

27 

28 

25.96 

10.49 

25.92 

10.60 

25.87 

10.72 

S25.82 

10.83 

28 

29 

26.89 

10.86 

26.84 

10.93 

26  .  79 

11.10 

!  26  .  74 

11.21 

29 

30    27.82 

11.24 

27.77 

11.36 

27.72 

11.48 

127.67 

11.60 

30 

31 

28  .  74 

11.61 

28.69 

11.74 

28.64 

11.86 

28  .  59 

11.99 

31 

32 

29.67 

11.99 

29.62 

12.12 

29.56 

12.25 

29.51 

12.37 

32 

33 

r.0.60 

12.36 

30.54 

12.50 

30.49 

12.63 

130.43 

12.76 

33 

34 

31.52 

12  .  74 

31.47 

12.87 

31.41 

13.01 

131.35 

13.15 

34 

35 

32.45 

13.11 

32  .  39 

13.25 

32.34 

13.39 

S32.28 

13.53 

35 

36 

33.33 

13.49 

33.32 

13.63 

.33.26 

13.78 

I  33  .  20 

13.92 

36 

37 

34.31 

13.86 

34.24 

14.01 

34.18 

14.16 

134.12 

14.31 

37 

38 

35  .  23 

14.24 

35.17 

14.39 

35  .  1  1 

14.54 

35  .  04 

14.70 

33 

39 

36.16 

14.61 

36.10 

14.77 

36.03 

14.92 

35.97 

15.08 

39 

40 

37.09 

14.98 

37.02 

15.15 

36.  98 

15.31 

36.89 

15.47 

40 

41 

33.01  !  15.36 

37.95 

15.52 

37.88 

15.69 

37.81 

15.88 

41 

42 

38.94  I  15.73 

38.87 

15.90 

33.80 

16.07 

33  .  73 

16.24 

42 

43 

39.87  1  16.11 

39.80 

16.23 

39  .  73 

16.46 

39.65 

16.63 

43 

44 

40.80  1  16.48 

40.72 

16.66 

40  .  65 

16.84 

40.58 

17.02 

44 

45 

41.72  .16.86 

41.65 

17.04 

41.57 

17.22 

41.50 

17.40 

45 

46 

42.65  !  17.23 

42  .  57 

17.42 

42.50 

17.60 

4-2.42 

17.79 

46 

47 

43.58  i  17.61 

43.50 

17.80 

43.42 

17.99 

43.34 

18.18 

47 

48  |44.50  i  17.98 

44.43 

18.18 

44.35 

18.37 

44.27 

18.56 

48 

49 

45.43  i  18.36 

45.35 

]  8  .  55 

45.27. 

18.75 

45.19 

18.95 

49 

50 

46.36  l  18.73 

46.28 

18.93 

46.19 

19.13 

46.11 

19.34 

50 

o 
o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

CD 

O 

q 

i 

1 

to 

5 

68  Deg. 

67  1  Deg. 

G7£  Deg. 

67i  Deg. 

fi 

1 

TRAVERSE  TABLE. 


47 


o 

OB" 

22  Deg. 

22J  Deg. 

221  Deg. 

22|  Deg. 

0 
5' 

P 

3 
O 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 
o 

CD 

~5~T 

47.29 

19.10 

47.20 

19.31 

47.12 

19.52 

47.03 

19.72 

~5T 

52 

48,21 

19.48 

48.13 

19.69 

48.04 

19.90 

47.95 

20.11 

52 

53 

49.14 

19.85 

49.05 

20.07 

48.97 

20.28 

48.88 

20.50 

53 

54 

50.07 

20.23 

49.98 

20  .45 

49.89 

20.66 

49.80 

20.88 

54 

55 

51.00 

20.60 

50.90 

20.83 

50.81 

21.05 

50.72 

21.27 

55 

56 

51.92 

20.98 

51.83 

21.20 

51.74 

21.43 

51.64 

21.66 

58 

57 

52.85 

21.35i 

52.76 

21.58 

52.66 

21.81 

52.57 

22.04 

57 

58 

53.78 

21.73 

53.68 

21.96 

53.59 

22.20 

53.49 

22.43 

58 

59  154.70 

22.10 

54.61 

22.34 

54.51 

22.58 

54.41 

22  .82 

59 

60  155.63    22.48 

55  .  53 

22  .  72 

55.43 

22.96 

55.33 

23.20 

60 

"61 

56.56 

22.85 

56.47 

23.10 

56  .  36 

23.34 

56.25 

23.59 

61 

62 

57.49 

23.23 

57.38 

23.48 

57.28 

23.73 

57.18 

23.98 

62 

63 

58.41 

23  .  60 

58.31 

23  .  85 

58.20 

24.11 

58.10 

24.36 

63 

64 

59.34 

23.97 

59  .  23 

24.23 

59.13 

24.49 

59.02 

24.75 

64 

65 

60.27 

24.35 

60.16 

24.61 

60.05 

24.87 

59.94 

25  .  14 

65 

66 

61.19 

24.72 

61.09 

24.99 

60.98 

25.26 

60.87 

25.52 

66 

67 

62.12 

25.10 

62.01 

25.37 

61.90 

25  .  64 

61.79 

25.91 

67 

63 

63.05 

25.47 

62.94 

25.75 

62.82 

26.02 

62.71 

26.30 

68 

69 

63  .  98 

25.85 

63.86 

26.13 

63.75 

26.41 

63.63 

26.68 

69 

70 

64.90 

26.22 

64.79    26.51 

64.67 

26.79 

64.55 

27.07 

70 

~71 

65  .  83 

26  .  60 

65.71.    26.88 

65.60 

27.17 

65.48 

27.46 

71 

72 

66.76 

26.97 

66.64 

27.26 

66  .  52 

27.55 

66.40 

27.84 

72 

73 

67.63 

27.35 

67.56 

27.64 

67.44 

27.94 

67.32 

28.23 

73 

74 

68.61 

27.72 

68.49 

28.02 

68.37 

28.32 

68.24 

28.62 

74 

75 

69.54 

.28.10 

69.42 

28.40 

69.29 

23.70 

69.17 

29.00 

75 

76 

70.47 

28.47 

70.34 

23  .  78 

70.21 

29.08 

70.09 

29.39 

76 

77 

71.39 

28.84 

71.27 

29.16 

71.14 

29.47 

71.01 

29  .  78 

77 

73 

72.32 

29.22 

72.19 

29.53 

72.06 

29.85 

71.93 

30.16 

78 

'  79 

73.25 

29.59 

73.12 

29.91 

72.99 

30.23 

72.85 

30.55 

79 

80 

74.17 

29.97 

74.04 

30.29 

73.91 

30.61 

73.78 

30.94 

80 

81 

75.10 

30.34 

74.97 

30.67 

74.83 

31.00 

74.70 

31.32 

81 

82 

76.03 

30.72 

75.89 

31.05 

75  .  76 

31.38 

75.62 

31.71 

82 

83 

76.96 

31.09 

76.82 

31.43 

76.68 

31.76 

76.54 

32.10 

83 

84 

77.88 

31.47 

77.75 

31.81 

77.61 

32.15 

77.46 

32.43 

84 

85 

78.81 

31.84 

78.67 

32.19 

78.53 

32.53 

78.39 

32.87 

85 

86 

79.74 

32.22 

79.60 

32.56 

79.45 

32.91 

79.31 

33.26 

86 

87 

80.66 

32  .  59 

80  .  52 

32  .  94" 

80.38 

33.29 

80.23 

33.64 

87 

83 

Si  159 

32.97 

81.45 

33  .  32 

81.30 

33.68 

81.15 

34.03 

88 

89 

82.52 

33.34 

82.37 

33.70 

82.23 

34.06 

82.08 

34.42 

89 

90 

83.45 

33.71 

83.30 

34.08 

83.15 

34.44 

83.00 

34.80 

90 

91 

84.37 

34.09 

84.22 

34.46 

84.07 

34.82 

83.92 

35.19 

91 

92 

85.30 

34.46 

85.15 

34.84 

85.00 

35.21 

84.84 

35.58 

92 

93    86.23 

34.84 

86.08    35.21 

85.92 

35  .  59 

85  .  76 

35.  9G 

93 

94    87.16 

35.21 

87.  00  I  35.59 

86.84 

35.97 

86.69 

38.35 

94 

95  |83.08 

35.59 

87.93    35.97 

87.77 

36.35 

87.61 

36.74 

95 

96  !  89.01 

35.96 

88.85    36.35 

88.69 

36.74 

88.53 

37.12 

96 

97    89.94 

36.34 

89.78 

36.73 

89.62 

37.12 

89.45 

37.51 

97 

93 

90.86 

36.71 

90.70    37.11 

90.54 

37.50 

90.38 

37.90 

98 

99 

91.79 

37.09 

91.63    37.49 

'91.46 

37.89 

91.30 

38.28 

99 

100 

92.72 

37.46 

92.55    37.86 

i92.39 

38.27 

92.22    38.67 

100 

1 

Dep. 

Lat. 

Dep. 

Lat.« 

D*ep. 

Lat. 

Dep. 

Lat. 

aj 
o 

q 

ci 

i   5 

68  Deg. 

67|  Deg. 

671  Deg. 

67*  Deg. 

p 

TRAVERSE   TABLE 


q 

23  Deg. 

23}  Deg. 

23£  Deg. 

23|  Deg. 

O 

p* 

1 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

i 

0.92 

0.39 

0.92 

0.39 

0.92 

~Ob~ 

0.92 

0.40 

1 

2 

1.84 

0.78 

1.84 

0.79 

1.83 

0.80 

1.83 

0.81 

2 

3 

2.76 

1.17 

2.76 

1.18 

2.75 

1.20 

2.75 

1.21 

3 

4 

3.68 

1.56 

3.68 

1.58 

3.67 

1.59 

3.66 

1.61 

4 

5 

4.60 

1.95 

4.59 

1.97 

4.59 

1.99 

4.58 

2.01 

5 

6 

5.52 

2.34 

5.51 

2.37 

5.50 

2.39 

5.49 

2.42 

6 

7 

6.44 

2.74 

6.43 

2.76 

6.42 

2.79 

6.41 

2.82 

7 

8 

7.36 

3.13 

7.35 

3.16 

7.34 

3.19 

7.32 

3.22 

8 

9 

8.28 

3.52 

8.27 

3.55 

8.25 

3.59 

8.24 

3.62 

9 

10 

9.20 

3.91 

9.19 

3.95 

9.17 

3.99 

9.15 

4.03 

10 

11 

10.13 

4.30 

10.11 

4.34 

10.09 

4.39 

10.07 

4.43 

11 

12 

11.05 

4.69 

11.03 

4.74 

11.00 

4.78 

10.98 

4.83 

12 

13 

11.97 

5.08 

11.94 

5.13 

11.92 

5.18 

11.90 

5.24 

13 

14 

12.89 

5.47 

12.86 

5.53 

12.84 

5.58 

12.81 

5.64 

14 

15 

13.81 

5.86 

13.78 

5.92 

13.76 

5.98 

13.73 

6.04 

15 

16 

14.73 

6.25 

14.70 

6.32 

14.67 

6.38 

14.64 

6.44 

16 

17 

15.65 

6.64 

15.62 

6.71 

15.59 

6.78 

15.56 

6,85 

17 

18 

16.57 

7.03 

16.54 

7.11 

16.51 

7.18 

16.48 

7.25 

18 

19 

17.49 

7.42 

17.46 

7.50 

17.42 

7.58 

17.39 

7.65 

19 

20 

18.41 

7.81 

18.38 

7.89 

18.34 

7.97 

18.31 

8.05 

20 

21 

19.33 

8.21 

19.29 

8.29 

19.26 

8.37 

19.22 

8.46 

21 

22 

20.25 

8.60 

20.21 

8.68 

20.18 

8.77 

20.14 

8.86 

22 

23 

21.17 

8.99 

21.13 

9.08 

21.09 

9.17 

21.05 

9.26 

23 

24 

22.09 

9.38 

22.05 

9.47 

22.01 

9.57 

21.97 

9.67 

24 

25 

23.01 

9.77 

22.97 

9.87 

22.93 

9.97 

22.88 

10.07 

25 

26  123.93 

10.16 

23.89 

10.26 

23.84 

10.37 

23.80 

10.47 

26 

27 

24.85 

10.55 

24.81 

10.66 

24.76 

10.77 

24.71 

10.87 

27 

28 

25.77 

10.94 

25.73 

11.05 

25.68 

11.16 

25.63 

1  .1  .-28 

28 

29 

26.69 

11.33 

26.64 

11.45 

26.59 

11.56 

26.54 

11.68 

29 

30 

27.62 

11.72 

27.56 

11.84 

27.51 

11.96 

27.46 

12.08 

30 

31 

28.54 

12.11 

28.48 

12.24 

28.43 

12.36 

28.37 

12.49 

31 

32 

29.46 

12.50 

29.40 

12.63 

29.35 

12.76 

29.29 

12.89 

32 

33 

30.38 

12.89 

30.32 

13.03 

30.26 

IS.lo 

30.21 

13.29 

33 

34 

31.30 

13.28 

31.24 

13.42 

31.18 

13.56 

31.12 

13.69 

34 

35 

32.22 

13.68 

32.16 

13.82 

32.10 

13.96 

32.04 

14.10 

35 

36 

33.14 

14.07 

33.08 

14.21 

33.01 

14.35 

32.95 

14.50 

36 

37 

34.06 

14.46 

34.00 

14.61 

33.93 

14.75 

33.87 

14.90 

37 

38 

34.98 

14.85 

34.91 

15.00 

34.85 

15.15 

34.78 

15.30 

38 

39 

35.90 

15.24 

35.83 

15.39 

35.77 

15.55 

35.70 

15.71 

39 

40 

36.82 

15.63 

36.75 

15.79 

36.68 

15.95 

36.61 

16.11 

40 

41 

37.74 

16.02 

37.67 

16.18 

37.60 

16.35 

37.53 

16.51 

41 

42 

38.66 

16.41 

38.59 

16.58 

38.52 

16.75 

38.44 

16.92 

42 

43 

39.58 

16.80 

39.51 

16.97 

39.43 

17.15 

39.36 

17.32 

43 

44 

40.50 

17.19 

40.43 

17.37 

40.35 

17.54 

40.27 

17.72 

44 

45 

41.42 

17.58 

41.35 

17.76 

41.27 

17.94 

41.19 

18.12 

45 

46 

42.34 

17.97 

42.26 

18.16 

42.18 

18.34 

42.10 

18.53 

46 

47 

43.26 

18.36 

43.18 

18.55 

43.10 

18.74 

43.02 

18.93 

47 

48 

44.18 

18.76 

44.10 

18.95 

44.02 

19.14 

43.93 

19.33 

48 

49 

45.10 

19.15 

45.02 

19.34 

44.94 

19.54 

44.85 

19.73 

49 

50    46.03 

19.54 

45  .  94 

19.74 

45.85 

19.94 

45.77 

20.14 

50 

1 

Dep. 

Lat. 

Dep.      Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

g-         67  Deg. 

66|  Deg. 

66£  Deg. 

66}  Deg. 

2 

TRAVERSE   TABLE, 


49 


o 

23  Deg. 

23i  Deg. 

23£  Deg. 

23|  Deg. 

? 

3 
a 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o  • 

51 

46.95 

19.93 

46.86 

20.  13 

46.77 

20.34 

46.68 

20.54 

51 

52 

47.87 

20.32 

47.78 

20.53 

47.69 

20.73 

47.60 

20.94 

52 

53 

48.79 

20.71 

48.70 

20.92 

48.60 

21.13 

48.51 

21.35 

53 

54 

49.71 

21.10 

49.61 

21.32 

49.52 

21.53 

49.43 

21.75 

54 

55 

50.63 

21.49 

50.53 

21.71 

50.44 

21.93 

50.34 

22.15 

55 

56 

51.55 

21.88 

51.45 

22,11 

51.36 

22.33 

51.26 

22.55 

56 

57 

52.47 

22.27 

52.37 

22.50 

52.27 

22.73 

52.17 

22.96 

57 

58 

53.39 

22.66 

53.29 

22.90 

53.19 

23.13 

53.09 

23.36 

58 

59 

54.31 

23.05 

54.21 

23.29 

54.11 

23.53 

54.00 

23.76 

59 

60 

55.23 

23.44 

55.13 

23.68 

55.02 

23.92 

54.92 

24.16 

60 

61 

56.15 

23.83 

56.05 

24.08 

55.94 

24.32 

55.83 

24.57 

6* 

62 

57.07 

24.23 

56.97 

24.47 

56.86 

24.72 

56.75 

24.97 

62 

63 

57.99 

24.62 

57.88 

24.87 

57.77 

25.12 

57.66 

25.37 

63 

64 

53.91 

25.01 

58.80 

25.26 

58.69 

25.52 

58.58 

25.78 

64 

65 

59.83 

25.40 

59.72 

25.66 

59.61 

25.92 

59.50 

26.18 

65 

66 

60.75 

25  .  79 

60.64 

26.05 

60.53 

26.32 

60.41 

26.58 

66 

67 

61.67 

26.18 

61.56 

28.45 

61.44 

26.72 

61.33 

26.98 

67, 

68 

62.59 

26.57 

62.48 

26.84 

62.36 

27.11 

62.24 

27.39 

68 

69 

63.51 

26.96 

63.40 

27.24 

63.28 

27.51 

63.16 

27.79 

69 

70 

64.44 

27.35 

64.32 

27.63 

64.19 

27.91 

64.07 

28.19 

70 

71 

65.36 

27.74 

65.23 

28.03 

65.11 

28.31 

64.99 

28.59 

71 

72 

66.28 

28.13 

66.15 

28.42 

66.03 

28.71 

65.90 

29.00 

72 

73 

67.20 

28.52 

67.07 

28.82 

66.95 

29.11 

66.82 

29.40 

73 

74 

68.12 

28.91 

67.99 

29.21 

67.86 

29.51 

67.73 

29.80 

74 

75 

69.04 

29.30 

68.91 

29.61 

68.78 

29.91 

68.65 

30.21 

75 

76 

69.96 

29.70 

69.83 

30.00 

69.70 

30.30 

69.56 

30.61 

76 

77 

70.88 

30.09 

70.75 

30.40 

70.61 

30.70 

70.48 

31.01 

77 

78 

71.80 

30.48 

71.67 

30.79 

71.53 

31.10 

71.39 

31.41 

78 

79 

72.72 

30.87 

72.58 

31.18 

72.45 

31.50 

72.31 

31.82 

79 

80 

73.64 

31.26 

73.50 

31.58 

73.36 

31.90 

73.22 

32.22 

80 

81 

74.56 

31.65 

74.42 

31.97 

74.28 

32.30 

74.14 

32.62 

81 

82 

75.48 

32.04 

75.34 

32.37 

75.20 

32.70 

75.06 

33.03 

82 

83 

76.40 

32.43 

76.26 

32.76 

76.12 

33.10 

75.97 

33.43 

83 

84 

77.32 

32.82 

77.18 

33.16 

77.03 

33.49 

76.89 

33.83 

84 

85 

78.24 

33.21 

78.10 

33.55 

77.95 

33.89 

77.80 

34.23 

85 

86 

79.16 

33.60 

79.02 

33.95 

78.87 

34.29 

78.72 

34.64 

86 

87 

80.08 

33.99 

79.93 

34.34 

79.78 

34.69 

79.63 

35.04 

87 

88 

8J.OO 

34.38 

80.85 

34.74 

80.70 

35.09 

80.55 

35.44 

88 

89 

81.92 

34.78 

81.77 

35.13 

81.62 

35.49 

81.46 

35.84 

89 

90 

82.85 

35.17 

82.69 

35.53 

82.54 

35.89 

82.38 

36.25 

90 

91 

83.77 

35.56 

83.61 

35.92 

83.45 

36  .  29 

83.29 

36.65 

91 

92 

84.69 

35.95 

84.53 

36.32 

84.37 

36.68 

84.21 

37.05 

92 

93 

85.61 

36.34 

85.45 

36.71 

85.29 

37.08 

85.12 

37.46 

93 

94 

86.53 

36.73 

86.37 

37.11 

86.20 

37.48 

86.04 

37.86 

94 

95 

87.45 

37.12 

87.29 

37.50 

87.12 

37.88 

86.95 

38.26 

95 

96 

88.37 

37.51 

88.20 

37.90 

88.04 

38.28 

87.87 

38.66 

96 

97 

89.29 

37.90 

89.12 

38.29 

88.95 

38.68 

88.79 

39.07 

97 

98 

90.21 

38.29 

90.04 

38.68 

89.87 

39.08 

89.70 

39.47 

98 

99 

91.13 

38.68 

90.96 

39.08 

90.79 

39.48 

90.62 

39.87 

99 

100 

92.05 

39.07 

91.88 

39.47 

91.71 

39.87 

91.53 

40.27 

100 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

5 

1 

S 

67  Deg. 

66|  Deg. 

661  Deg. 

66J  Deg. 

s 

60 


TRAVERSE   TABLE 


o 

24  Deg. 

24J  Deg. 

24iDeg. 

24$  D»g. 

£ 

? 

r 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

j 

i 

0.91 

0.41 

0.91 

0.41 

0.91 

0.41 

0.91 

0.42 

i 

2 

1.83 

0.81 

1.82 

0.82 

1.82 

0.83 

1.82 

0.84 

2 

3 

2.74 

1.22 

2.74 

1.23 

2.73 

1.24 

2.72 

1.26 

3 

4 

3.65 

1.63 

3.65 

1.64 

3.64 

1.66 

3.63 

1.67 

4 

5 

4.67 

2.03 

4.56 

2.05 

4.55 

2.07 

4.54 

2.09 

5 

6 

5.48 

2.44 

5.47 

2.46 

5.46 

2.49 

5.45 

2.51 

6 

7 

6.39 

2.85 

6.38 

2.87 

6.37 

2.90 

6.36 

2.93J       7 

8 

7.31 

3.25 

7.29 

3.29 

7.28 

3.32 

7.27 

3.35 

8 

9 

8.22 

3.66 

8.21 

3.70 

8.19 

3.73 

8.17 

o.77 

9 

10 

9.14 

4.07 

9.12 

4.11 

9.10 

4.15 

9.08 

4.19!     10 

11 

10.05 

4.47 

10.03 

4.52 

10.01 

4.56 

9.99 

4.61  i     11 

12 

10.96 

4.88 

10.94 

4.93 

10.92 

4.98 

10.90 

5.02!     12 

13 

11.88 

5.29 

11.85 

5.34 

11.83 

5.39 

11.81 

5.44 

13 

14 

12.79 

5.69 

12.76 

5.75 

12.74 

5.81 

12.71 

5.86 

14 

15 

13.70 

6.10 

13.68 

6.16 

13.65 

6.22 

13.62 

6.28 

15 

16 

14.62 

ft.  51 

14.59 

6.57 

14.56 

6.64 

14.53 

6.70 

16 

17 

15.53 

6.S2 

15.50 

6.98 

15.47 

7.05 

15.44 

7.12 

17 

18 

16.44 

7.32 

16.41 

7.39 

16.38 

7.46 

16.35 

7.54 

18 

19 

17.36 

7.73 

17.32 

7.80 

17.29 

7.88 

17.25 

7.95 

19 

20 

18.27 

8.13 

18.24 

8.21 

18.20 

8.29 

18.16 

8.37 

20 

21 

19.18 

8.54 

19.15 

8.63 

19.11 

8.71 

19.07 

8.79 

21 

22 

20.10 

8.95 

20.06 

9.04 

20.02 

9.12 

19.98 

9.21 

22 

23 

21.01 

9.35 

20.97 

9.45 

20.93 

9.54 

20.89 

9.63 

23 

24 

21.93 

9.76 

21.88 

9.86 

21.84 

9.95 

21.80 

10.05 

24 

25 

22.84 

10.17 

22.79 

10.27 

22.75 

10.37 

22.70 

10.47 

25 

26 

23.75 

10.58 

23.71 

10.68 

23.66 

10.78 

23.61 

10.89 

26 

27 

24.67 

10.98 

24.62 

11.09 

24.57 

11.20 

24.52 

11.30 

27 

28 

25.58 

11.39 

25.53 

11.50 

25.48 

11.61 

25.43 

11.72 

28 

29 

26.49 

11.80 

26.44 

11.91 

26.39 

12.03 

26.34 

12.14 

29 

30 

27.41 

12.20 

27.35 

12.32 

27.30 

12.44 

27.24 

12.56 

30 

31 

28,32 

12.61 

28.26 

12.73 

28.21 

12.86 

28.15 

12.98 

31 

32 

29.23 

13.02 

29.18 

13.14 

29.12 

13.27 

29.06 

13.40 

32 

33 

30.15 

13.42 

30.09 

13.55 

30.03 

13.68 

29.97 

13.82 

33 

34 

31.06 

13.83 

31.00 

13.96 

30.94 

14.10 

30.88 

14.23 

34 

35 

31.97 

14.24 

31.91 

14.  38 

31.85 

14:51 

31.78 

14.65 

35 

36 

32.89 

14.64 

32.82 

14:79 

32.76 

14.93 

32.69 

15.07 

36 

37 

33.80 

15.05 

33.74 

15.20 

33.67 

15.34 

33.60 

15.49 

37 

38 

34.71 

15.46 

34.65 

15.61 

34.58 

15.76 

34.51 

15.91 

38 

39 

35.63 

15.86 

35.56 

16.02 

35.49 

16.17 

35.42 

18.33 

39 

40 

36.54 

16.27 

36.47 

16.43 

36.40 

16.59 

36.33 

16.75 

40 

41 

37.46 

16.68 

37.38 

16.84 

37.31 

17.00 

37.23 

17,16 

41 

42 

38.37 

17.08 

38.29 

17.25 

38.22 

17.42 

38.14 

17.58 

42 

43 

39.28 

17.49 

39.21 

17.60 

39.13 

17.83 

39.05 

18.00 

43 

44 

40.20 

17.90 

40.12 

18.07 

40.04 

18.25 

39.96 

18.42 

44 

45 

41.11 

18.30 

41.03 

18.48 

40.95 

18.66 

40.87 

18.84 

45 

46 

42.02 

18.71 

41.94 

18.89 

41.86 

19^.08 

41.77 

19.26 

46 

47 

42.94 

19.12 

42.85 

19.30 

42.77 

19^.49 

42.68 

19.68 

47 

48 

43.85 

19.52 

43.76 

19.71 

43.68 

19.91 

43.59 

20.10 

48 

49 

44.76 

19.93 

44.68 

20.13 

44.59 

20.32 

44.50 

20.51 

49 

50 

45.68 

20.34 

45.59 

20.54 

45.50 

20.73 

45.41 

20.93 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

cd 

1 

s 

66  Deg. 

6'5|  Deg. 

65  1  Deg. 

65i  Deg. 

Q 

TRAVERSE    TABLE. 


3 

5i* 

a 
o 

~51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

"61 

62 
63 
64 
65 
66 
67 
68 
69 
70 

24  Deg. 

24}  Deg. 

24i  Deg. 

24|  Deg. 

O 

5* 

p 
p 
a 
?  • 
~5~I 
52 
53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 

71 
72 
73 
74 
75 
76 
77 
78 
79 
80 
81 
82 
83 
84 
85 
86 
87 
88 
89 
90 
91 
92 
93 
94 
95 
96 
97 
98 
99 
100 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

46.  53 
47.50 
48.42 
49.33 
50.24 
51.16 
52  .  07 
52.99 
53.90 
54.81 

20.74 
21.15 
21.56 
21.96 
22.37 
22.78 
23.18 
23.59 
24.00 
24.40 

46.50 
47.41 
48.32 
49.24 
50.15 
51.06 
51.97 
52.88 
53.79 
54.71 

20.95 
21.36 
21.77 
22.18 
22.59 
23.00 
23.41 
23.82 
24.23 
24.64 

46.41 
47.32 

48.23 
49.14 
50.05 
50.96 
51.87 
52  .  78 
53.69 
54.60 

21.15 
21.56 
21.98 
22.39 
22.81 
23.22 
23.64 
24.05 
24.47 
24.88 

46.32 
47.22 
48.13 
49.04 
49.95 
50.86 
51.76 
52.67 
53.58 
64.49 

21.35 
21.77 
22.19 
22.61 
23.03 
23.44 
23.86 
24.28 
24.70 
25.12 

55  .  73 
56.64 
57.55 
58.47 
59.38 
60.29 
61.21 
62.12 
63.03 
63.95 

24.81 
25.22 
25.62 
26.03 
26.44 
26.84 
27.25 
27.66 
28.06 
28.47 

55.62 
56.53 
57.44 
58.35 
59.26 
60.18 
61.09 
62.00 
62.91 
63.82 

25.05 
25.46 

25.88 
26.29 
26.70 
27.11 
27:52 
27.93 
28.34 
28.75 

55.51 
56.42 
57.33 
58  .  24 
59.15 
60.06 
60.97 
61.88 
62.79 
63.70 

25.30 
25.71 
26.13 
26  /54 
26.96 
27.37 
27.78 
28.20 
28.61 
29.03 

55.40 
56.30 
57.21 
58.12 
59.03 
59.  S4 
60.85 
61.75 
62.66 
63.57 
~64.48 
65.39 
66.29 
67.20 
68.11 
69.02 
69.93 
70.84 
71.74 
72.65 

25.54 
25.96 
26.38 
26  .  79 
27.21 
27.63 
28.05 
28.47 
28.89 
29.31 

71 
72 
73 
74 
75 
76 
77 
78 
79 
80 

64.86 
65  .  78 
66.69 
67.60 
68.52 
69.43 
70.34 
71.26 
72.17 
73.08 

28.88 
29.28 
29.69 
30.10 
30.51 
30.91 
31.32 
31.73 
32.13 
32.54 

64.74 
65.65 
66.56 
67.47 
68.38 
69.29 
70.21 
71.12 
72.03 
72.94 

29.16 
29.57 
29.98 
30.39 
30.80 
31.21 
31.63 
32.04 
32.45 
32.86 

64.61 
65.52 
66.43 
67.34 

68.25 
69.16 
70.07 
70.98 
71.89 
72.80 

29.44 
29.86 
30.27 
30.69 
31.10 
31.52 
31.93 
32.35 
32.76 
33.18 

29.72 
30.14 
30.56 
30.98 
31.40 
31.82 
32.24 
32.66 
33.07 
33.49 

81 
82 
83 
84 
85 
88 
87 
88 
89 
90 

91 
92 
93 
94 
95 
96 
97 
98 
99 
100 

74.00 
74.91 
75.82 
76  .  74 
77.65 
78.56 
79.48 
80.39 
81.31 
82.22 

32.95 
33.35 
33.76 
34.17 
34.57 
34.98 
35.39 
35.79 
36.20 
36.61 

73.85 
74.76 
75.68 
76.59 
77.50 
78.41 
79.32 
80.24 
81.15 
82.06 

33.27 
33  .  68 
34.09 
34.50 
34.91 
35.32 
35.73 
36.14 
36.55 
36.96 

73.71 

74.62 
75.53 
76.44 
77.35 
78  26 
79.17 
80.08 
80.99 
81.90 

33.59 
34.00 
34.42 
34.83 
35.25 
35,66 
36.08 
36.49 
36.91 
37.32 

73.56 
74.47 
75.38 
76.28 
77.19 
78.10 
79.01 
79.92 
80.82 
81.73 

33.91 
34.33 
34.75 
35.17 
35.59 
36.00 
36.42 
36.84 
37.26 
37.68 

83.13 
84.05 
84.96 
85.87 
86.79 
87.70 
88.61 
89.53 
90.44 
91.35 

37.01 
37.42 
37.83 
38  .23 
38.64 
39.05 
39.45 
39.86 
40.27 
40.67 

82.97 
83.88 
84.79 
85.71 
86.62 
87.53 
88.44 
89.35 
90.26 
91.18 

37.38 
37.79 
38.20 
38.61 
39.02 
39.43 
39,84 
40.25 
40.66 
41.07 

82.81 
83.72 
84.63 
85.54 
86.45 
87.36 
88.27 
89.18 
90.09 
91.00 

37.74 
38.15 
38.57 
38.98 
39.40 
39.81 
40.23 
40.64 
41.05 
41.47 

82.64 
83.55 
84.46 
85.37 
86.27 
87.18 
88.09 
89.00 
89.91 
90.81 

33.10 
38.52 
38.94 
39.35 
39.77 
40.19 
40-.  61 
41.03 
41.45 
41.87 

b 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Q 

66  Deg. 

65|  Deg, 

65^  Deg. 

654  Deg. 

i-y* 

TRAVERSE 


I 

25  Deg. 

25*  Deg. 

25i  Deg. 

25|  Deg. 

gf 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

*i 

0.91 

0.42 

O.SO 

0.43 

0.90 

0.43 

0.90 

0.43 

1 

2 

1.81 

0.85 

1.81 

0.85 

1.81 

0.86 

1.80 

0.87 

2 

3 

2.72 

1.27 

2.71 

1.28 

2.71 

1.29 

2.70 

1.30 

3 

4 

3.63 

1.69 

3.62 

1.71 

3,61 

1.72 

3.60 

1.74 

4 

5 

4.53 

2.11 

4.52 

2.  13 

4.51 

2.15 

4.50 

2.17 

5 

6 

5.44 

2.54 

5.43 

2.56 

5.42 

2.58 

5.40 

2,61 

6 

7 

6.34 

2.96 

6.33 

2.99 

6.32 

3.01 

6.30 

3.04 

7 

8 

7.25 

3.38 

7.24 

3.41 

7.22 

3.44 

7.21 

3.48 

8 

9 

8.16 

3.80 

8.14 

3.84 

8.12 

3.87 

8.11 

3.91 

9 

10 

9.06 

4.23 

9.04 

4.27 

9.03 

4.31 

9.01 

4.34 

1Q 

11 

9.97 

4.65 

9.95 

4.69 

9.93 

4.74 

9.91 

4.78 

11 

12 

10.88 

5.07 

10.85 

5,12 

10.83 

5.17 

10,81 

5.21 

12 

13 

11.78 

5.49 

11.76 

5.55 

11.73 

5.60 

11.71 

5.65 

13 

14 

12.69 

5.92 

12.66 

5.97 

12.64 

6.03 

12.61 

6.08 

14 

15 

13.59 

6.34 

13.57 

6.40 

13.54 

6.46 

13.51 

6.52 

15 

16 

14.50 

6.76 

14.47 

6.83 

14.44 

6.89 

14.41 

6.95 

16 

17 

15.41 

7.18 

15.38 

7.25 

15.34 

7.32 

15.31 

7.39 

17 

18 

16.31 

7.61 

16.28 

7.68 

16.25 

7.75 

16.21 

7.82 

18 

19 

17.22 

8.03 

17.18 

8.10 

17.15 

8.18 

17.11 

8.25 

19 

20 

18.13 

8.45 

18.09 

8.53 

18.05 

8.61 

18.01 

8.69 

20 

21 

19.03 

8.87 

18.99 

8.96 

18.95 

9.04 

18.91 

9.12 

21 

22 

19.94 

9.30 

19.90 

9.38 

10.86 

9.47 

19.82 

9.56 

22 

23 

20.85 

9.72 

20.80 

9.81 

20.76 

9.90 

20.72 

9.99 

23 

24 

21.75 

10.14 

21.71 

10.24 

21.66 

10.33 

21.62 

10.43 

24 

25 

22.66 

10.57 

22.61 

10.66 

22.56 

10.76 

22.52 

10.86 

25 

26 

23.56 

10.99 

23.52 

11.09 

23.47 

11.19 

23.42 

11.30 

26 

27 

24.47 

11.41 

24.42 

11.52 

24.37 

11.62 

24.32 

11.73 

27 

28 

25.38 

11.83 

25,32 

11.94 

25.27 

12.05 

25.22 

12.16 

28 

29 

26.28 

12.26 

26.23 

12.37 

26.17 

12.48 

26.12 

12.60 

29 

30 

27.19 

12.68 

27.13 

12.80 

27.08 

12.92 

27.02 

13.03 

30 

31 

28.10 

13.10 

28.04 

13.22 

27.98 

13.35 

27.92 

13.47 

31 

32 

29.00 

13.52 

28.94 

13.65 

28.88 

13.78 

28.82 

13.90 

32 

33 

29  9J 

'3.95 

29.85 

14.08 

29.79 

14.21 

29.72 

14.34 

33 

34 

30.31 

.4.37 

30.75 

14.50 

30.69 

14.64 

30.62 

14.77 

34 

35 

31.72 

14.79 

31.66 

14.93 

31.59 

15.07 

31.52 

15.21 

35 

36 

32.63 

15.21 

32.56 

15.36 

32.49 

15.50 

32.43 

15.64 

36 

37 

33.53 

15.64 

33.46 

15.78 

33.40 

15.93 

33.33 

16.07 

37 

38 

34.44 

16.06 

34.37 

16.21 

34.30 

16.36 

34.23 

16.51 

38 

39 

35.35 

16.48 

35.27 

16.64 

35.20 

16.79 

35.13 

16.94 

39 

40 

36.25 

16.90 

36.18 

17,06 

36.10 

17.22 

36.03 

17.38 

40 

41 

37.16 

17.33 

37.09 

17.49 

37.01 

17.65 

36,93 

17.81 

41 

42 

38.06 

17.75 

37,99 

17.92 

37.91 

18.08 

37,83 

18.25 

42 

43 

38.97 

18.17 

38.89 

18.34 

38.81 

18.51 

38.73 

18,68 

43 

44 

39.88 

18.60 

39.80 

18.77 

39.71 

18.94 

39.63 

19.12 

44 

45 

40.78 

19.02 

40.70 

19.20 

40.62 

19.37 

40.53 

19.55 

45 

46 

41.69 

19.44 

41.60 

19.62 

41.52 

19.80 

41.43 

19.98 

46 

47 

42.60 

19.86 

42.51 

20.05 

42.42 

20.23 

42.33 

20.42 

47 

48 

43.50 

20.29 

43.41 

20.48 

43.32 

20.66 

43.23 

20.85 

48 

49 

44.41 

20.71 

44.32 

20.90 

44.23 

21.10 

44.13 

21.29 

49 

50 

45.32 

21.13 

45.22 

21.33 

45.13 

21.53 

45.03 

21.72 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

1 
5 

65  Deg. 

64|  Deg. 

64i  Deg. 

64*  Deg. 

P 

TRX 


ABLE. 


63 


g 

25  Deg. 

254  Deg. 

25i  Deg. 

25|  Deg. 

2- 

1 

r* 

s 
n 

CO 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

51 

46.22 

21.55 

46.13 

21.75 

146.03 

21.96 

45.94 

22.16 

51 

52 

47.13 

21.98 

47.03 

22.18 

46  .  93 

22.39 

46.84 

22.59 

52 

53 

48.03 

22.40 

47.94 

22.61 

47.84 

22.82 

47  ..74 

23.03 

53 

54 

48.94 

22.82 

48.84 

23.03 

48.74 

23.25 

48.64 

23.46 

54 

55 

49.85 

23.24 

49.74 

23.46 

49.64 

23.68 

49,54 

23.89 

55 

56 

50.75 

23.67 

50.65 

23.89 

50.54 

24.11 

50,44 

24.33 

56 

57 

51.66 

24,09 

51.55 

24.31 

51.45 

24.54 

51.34 

24.76 

57 

58 

52.57 

24.51 

52.46 

24.74 

52.35 

24.97 

52,24 

25.20 

58 

59 

53.47 

24.93 

53.36 

25.17 

53.25 

25.40 

53.14 

25.63 

59 

60 

54.38 

25.36 

54.27 

25.59 

54.16 

25.83 

54.04 

26.07 

60 

61 

55.28 

25.78 

55.17 

26.02 

55.06 

26.26 

54.94 

26.50 

61 

62 

56.19 

26.20 

56.08 

26.45 

55.96 

26.69 

55.84 

26.94 

62 

63 

57.10 

26.62 

56  .  98 

26.87 

56.86 

.27.12 

56,74 

27.37 

63 

64 

58.00 

27.05 

57.89 

27.30 

57.77 

27.55 

57.64 

27.80 

64 

65 

58.91 

27.47 

58.79 

27.73 

58.67 

27.98 

58.55 

28.24 

65 

66 

59.82 

27.89 

59.69 

28.15 

59.57 

28.41 

59.45 

28.67 

66 

67 

60  .  72 

28.32 

60.60 

28.58 

60.47 

28.84 

60.35 

29.11 

67 

68 

61.63 

28.74 

61.50 

29.01 

61.38 

29.27 

61.25 

29.54 

68 

69 

62.54 

29.16 

62.41 

29.43 

62.28 

29.71 

62.15 

29.98 

69 

70 

63.44 

29.58 

63.31 

29.86 

63.18 

30.14 

63.05 

30.41 

70 

71 

64.35 

30.01 

64.22 

30.29 

64.08 

30.57 

63.95 

30.85 

71 

72 

65.25 

30.43 

65.12 

30.71 

64.99 

31.00 

64.85 

31.28 

72 

73 

66.16 

30.85 

66.03 

31.14 

65.89 

31.43 

65  .  75 

31.71 

73 

74 

67.07 

31.27 

66.93 

31.57 

66.79 

31.86 

66.65 

32.15 

74 

75 

67.97 

31.70 

67.83 

31.99 

67.69 

32.29 

67.55 

32.58 

75 

76 

68.88 

32.12 

68.74 

32.42 

68.60 

32.72 

68.45 

33.02 

76 

77 

69.79 

32.54 

69.64 

32.85 

69.50 

33.15 

69.35 

33.45 

77 

78 

70.69 

32.96 

70.55 

33.27 

70.40 

33.58 

70.25 

33.89 

78 

79 

71.60 

33.39 

71.45 

33.70 

71.30 

34.01 

71.16 

34.32 

79 

80 

72.50 

33.81 

72.36 

34.13 

72.21 

34.44 

72  06 

34.76 

80 

81 

73.41 

34.23 

73.26 

34.55 

73.11 

34.87 

72.96 

35.19 

81 

82 

74.32 

34  .  65 

74.17 

34.98 

74.01 

35.30 

73.86 

35.62 

82 

83 

75.22 

35.08 

75.07 

35.41 

74.91 

35  .  73 

74.76 

36.06 

83 

84 

76.13 

35.50 

75.97 

35.83 

75.82 

36.16 

75.66 

36.49 

84 

85 

77.04 

35.92 

76.88 

36.26 

76.72 

36.59 

76.56 

36.93 

85 

86 

77.94 

36.35 

77.78 

36.68 

77.62 

37.02 

77.46 

37.36 

86 

87 

78.85 

36.77 

78.69 

37.11 

78.52 

37.45 

78.36 

37.80 

87 

88 

79  .  76 

37.19 

79.59 

37.54 

79.43 

37.88 

79.26 

38.23 

88 

89 

80.66 

37.61 

80.50 

37.96 

80.33 

38  .  32 

80.16 

38.67 

89 

90 

81.57 

38.04 

81.40 

38.39 

81.23 

38  .  75 

81.06 

39.10 

90 

91 

82.47 

38.46 

82.31 

38.82  | 

82.14 

39.18 

81.96 

39.53 

91 

92 

83.38 

38.88 

83.21 

39.24 

83.04 

39.61 

82.86 

39.97 

92 

93 

84.29 

39.30 

84.11 

39.67 

83.94 

40.04 

83.76 

40.40 

93 

94 

85.19 

39.73 

85.02 

40.10 

84.84 

40.47 

84.67 

40.84 

94 

95 

86.10 

40.15 

85.92 

40.52 

85.75 

40.90 

85.57 

41.27 

95 

96 

87.01 

40.57 

86.83 

40.95 

86.65 

41.33 

86.47 

41.71 

96 

97 

87.91 

40.99 

87.73 

41.38 

87.55 

41.76 

87.37 

42.14 

97 

98 

88.82 

41.42 

88.64 

41.80 

88.45 

42.19 

88.27 

42.58 

98 

99 

89.72 

41.84 

89.54 

42.23 

89.36 

42.62 

89.17 

43.01 

99 

100 

9.0.63 

42.26 

90.45 

42.66 

90.26 

43.05 

90.07 

43.44 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

8 

OJ 

to 

5 

65  Deg. 

64|  Deg. 

64i  Deg. 

64J  Deg. 

rt 

3 

TRAVERSE   TABLE. 


o 

26  Deg. 

264  Deg. 

26i  Deg. 

26|  Deg. 

q 

? 

£• 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1 

0.90 

0.44 

0.90 

0.44 

0.89 

0.45 

0.89 

0.45 

1 

2 

1.80 

0.88 

1.79 

0.88 

1.79 

0.89 

1.79 

0.90 

2 

3 

2.70 

1.32 

2.69 

1.33 

2.68 

1.34 

2.68 

1.35 

3 

4 

3.60 

1.75 

3.59 

1.77 

3.58 

1.78 

3.57 

1.80 

4 

5 

4.49 

2.19 

4.48 

2.21 

4.47 

2.23 

4.46 

2.25 

5 

6 

5.39 

2.63 

5.38 

2:65 

5.37 

2.68 

5.36 

2.70 

6 

7 

6.29 

3.07 

6.28 

3.10 

6.26 

3.12 

6.25 

3.15 

7 

8 

7.19 

3.51 

7.17 

3.54 

7.16 

3.57 

7.14 

3.60 

8 

9 

8.09 

3.95 

8.07 

3.98 

8.05 

4.02 

8.04 

4.05   9 

10 

8.99 

4.38 

8.97 

4.42 

8.95 

4.46 

8.93 

4.50  i  10 

11 

9.89 

4.82 

9.87 

4.87 

9.84 

4.91 

9.82 

4.95 

11 

12 

10.79 

5.26 

10.76 

5.31 

10.74 

5.35 

10.72 

5.40 

12 

13 

11.68 

5.70 

11.66 

5.75 

11.63 

5.80 

11.61 

5.85 

13 

14 

12.58 

6.14 

12.58 

6.19 

12.53 

6.25 

12.50 

6.30 

14 

15 

13.48 

6.58 

13.45 

6.63 

13.42 

6.69 

13.39 

6.75 

15 

16 

14.38 

7.01 

14.35 

7.08 

14.32 

7.14 

14.29 

7.20 

16 

17 

15.28 

7.45 

15.25 

7.52 

15.21 

7.59 

15.18 

7.65 

17 

18 

16.18 

7.89 

16.14 

7.96 

16.11 

8.03 

16.07 

8.10 

18 

19 

17.08 

8.33 

17.04 

8.40 

17.00 

8.48 

16.97 

8.55 

19 

20 

17.98 

8.77 

17.94 

8  .85 

17.90 

8.92 

17.86 

9.09 

20 

21 

18.87 

9.21 

18.83 

9.29 

18.79 

9.37 

18.75 

9.45 

21 

22 

19.77 

9.64 

19.73 

9.73 

19.69 

9.82 

19.65 

9.90 

22 

23 

20.67 

10.08 

20.63 

10.17 

20.58 

10.2-6 

20.54 

10.35 

23 

24 

21.5-7 

10.52 

21.52 

10.61 

21.48 

10.71 

21.43 

10.80 

24 

25 

22.47 

10.96 

22.42 

11.06 

22.37 

11.15 

22.32 

11.25 

25 

26 

23.37 

11.40 

23.32 

11,50 

23.27 

11.60 

23.22 

11.70 

26 

27 

24.27 

11.84 

24.22 

11.94 

24.16 

12.05 

24.11 

12.15 

27 

28 

25.17 

12.27 

25.11 

12.38 

25.06 

12.49 

25.00 

12.60 

28 

29 

26.06 

12.71 

26.01 

12.83 

25  .  95 

12.94 

25.90 

13.05 

29 

30 

26.96 

13.15 

26.91 

13.27 

26.85 

13.39 

26.79 

13.50 

30 

31 

27.86 

13.59 

27.80 

13.71 

27.74 

13.83 

27.68 

13.55 

31 

32 

28.76 

14.03 

28.70 

14.15 

28.64 

14.28 

28.58 

14.40 

32 

33 

29.66 

14.47 

29.60 

14.60 

29.53 

14.72 

29.47 

14.85 

33 

34 

30  .  56 

14.90 

30.49 

15.04 

30.43 

15.17 

30.36 

15.30 

34 

35 

31.46 

15.34 

31.39 

15.48 

31.32 

15.62 

31.25 

15.75 

35 

36 

32.36 

15.78 

32.29 

15.92 

32  .  22 

•16.06 

32.15 

16.20 

36 

37 

33.26 

16.22 

33.18 

16.36 

33  .  1  1 

16.51 

33.04 

16.65 

37 

38 

34.15 

16.66 

34.08 

16.81 

34.01 

16.96 

33.93 

17.10 

38 

39 

35.05 

17.10 

34.98 

17.25 

34.90 

17.40 

34.83 

17.55 

39 

40 

35.95 

17.53 

35.87 

17.69 

35.80 

17.85 

35.72 

18.00 

40 

41 

36.85 

17.97 

36.77 

18.13 

36.69 

18.29 

36.61 

18.45 

41 

42 

37.75 

18.41 

37.67 

18.58 

37.59 

18.74 

37.51 

18.90 

42 

43 

38.65 

18.85 

38.57 

19.02 

38.48 

19.19 

38.40 

19.35 

43 

44 

39.55 

19.29 

39.46 

19.46 

39.38 

19.63 

39.29 

19.80 

44 

45 

40.45 

19.73 

40.36 

19.90 

40  .  27 

20.08 

40.18 

20.25 

45 

46 

41'.  34 

20.17 

41.26 

20.35 

41.17 

20.53 

41.08 

20.70 

46 

47 

42.24 

20.60 

42.15 

20.79 

42.06 

20.97 

41.97 

21.15 

47 

48 

43.14 

21.04 

43.05 

2'.23 

42  .  96 

21.42 

42.86 

21.60 

48 

49 

44.04 

21.48 

43.95 

21.67 

43.85 

21.86 

43.76 

22.05 

49 

50 

44.94 

21.92 

44.84 

22.11 

44.75 

22.31 

44.65 

22.50 

50 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 
o 
C 

-*j 

1 

s 

64  Deg. 

63|  Deg. 

63£  Deg. 

63J  Deg. 

Q 

TRAVERSE    TABLE. 


g 

26  Deg. 

26*  Deg. 

26  £  Deg. 

2Cn)eg. 

3 

i 
P 

a. 

p 

3 
n 

O 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lit, 

Dep. 

5L 

45.84 

22.36 

45.74 

22.56 

45.64 

22.76 

45-54 

22796* 

~51 

52 

46.74 

22.80 

46.64 

23.00 

46.54 

23.20 

4G.43 

23.41 

52 

53 

47.64 

23.23 

47.53 

23.44 

47.43 

23.65 

47.33 

23.83 

53 

54 

48.53 

23.67 

48.43 

23.88 

48.33 

24.09 

48  22 

24.31 

54 

55 

49.43 

24.11 

49.33 

24.33 

49.22 

24.54 

49.11 

24.76 

55 

56 

50.33 

24.55 

50.22 

24.77 

50.12 

24.95 

50.01 

25.21 

56 

57 

51.23 

24.99 

51.12 

25.21 

51.01 

25-43 

50.00 

25.66 

57 

58 

52.13 

25.43 

52.02 

25.65 

51.91 

25  88 

51.79 

26.11 

58 

59 

53.03 

25.86 

52.92 

26.09 

52.80 

26-33 

52.69 

26  .  56 

59 

60 

53.93 

26.30 

53.81 

26.54 

53.70 

26-77 

53.58 

27.01 

60 

61 

54.83 

26.74 

54.71 

26.98 

54.59 

27.22 

54.47 

27.46 

61 

62 

55.73 

27.18 

55.61 

27.42 

55.49 

27.66 

55.36 

27.91 

62 

63 

56.62 

27.62 

56.50 

27.86 

56.38 

28.11 

56.26 

28.36 

63 

64 

57.52 

23.06 

57.40 

28.31 

57.28 

28.56 

57.15 

28.81 

64 

65 

58.42 

28.49 

58.30 

28.75 

58.17 

29.00 

58.04 

29.26 

65 

66 

59.32 

28.93 

59.19 

29.19 

59.07 

29.45 

58.94 

29.71 

66 

67 

60.22 

29.37 

60.09 

29.63 

59.96 

29.90" 

59.83 

30.16 

67 

68 

61.12 

29.81 

60.99 

30.08 

60.86 

30.34 

60.72 

30.61 

68 

69 

62.02 

30.25 

61.88 

30.52 

61.75 

30.79 

61.62 

31.06 

69 

70 

62.92 

30.69 

62.78 

30.96 

62.65 

31.23 

62.51 

31.51 

70 

71 

63.81 

31.12 

63.68 

31.40 

63.54 

31.68 

63.40 

31.96 

71 

72 

64.71 

31,56 

64.57 

31.84 

64.44 

32.13 

64.29 

32.41 

72 

73 

65.61 

32.00 

65.47 

32.29 

65.33 

32.57 

65.19 

32.86 

73 

74 

66.51 

32.44 

66.37 

32.73 

66.23 

33.02 

66.08 

33.31 

74 

75 

67.41 

32.88 

67.27 

33.17 

67.12 

33.46 

66.97 

33.76 

75 

76 

68.31 

33.32 

68.16 

33.61 

68.01 

33.91 

67.87 

34.21 

76 

77 

69.21 

33.75 

69.06 

34.06 

68.91 

34.36 

68.76 

34.66 

77 

78 

70.11 

34.19 

69.96 

34.50 

69.80 

34.80 

69.65 

35.11 

78 

79 

71.00    34.63 

70.85 

34.94 

70.70 

35.25 

70.55 

35.56 

79 

80 

71.90 

35.07 

71.75 

35.38 

71.59 

35.70 

71.44 

36.01 

80 

81 

72.80 

35.51 

72.65 

35  .  83 

72.49 

36.14 

72.33 

36.46 

81 

8^ 

73.70 

35.95 

73  .  54 

36.27 

73.38 

36.59 

73.22 

36.91 

82 

83 

74.60 

36.38 

74.44 

36.71 

74.28 

37.03 

74.12 

37.36 

83 

84 

75.50 

36.82 

75.34 

37.15 

75.17 

37.48 

75.01 

37.81 

84 

85 

76.40 

37.26 

76.23 

37.59 

76.07 

37.93 

75.90 

38.26 

85 

86 

77.30 

37.70 

77.13 

38.04 

76.96 

38.37 

76.80 

38.71 

86 

87 

78.20 

38.14 

78.03 

38.48 

77.86 

38.82 

77.69 

39.16 

87 

88 

79.09 

38.58 

78.92 

38.92 

78.75 

39.27 

78  .  58 

39.61 

88 

89 

79.99 

39.01 

79.82 

39  .  36 

79.65 

39.71 

79.48 

40.06 

89 

90 

80.89 

39.45 

,80.  72 

39.81 

80.54 

40.  1& 

80.37 

40.51 

90 

91 

81.79 

39.89 

81.62 

40.25 

81.44 

40.60 

81.26 

40.96 

91 

92 

82.69 

40.33 

82.51 

40.69 

82.33 

41.05 

82.15 

41.41 

92 

93 

83.59 

40.77 

83.41 

41.13 

83.23 

41.50 

83.05 

41.86 

93 

94 

84.49 

41.21 

84.31 

41.58 

84.12 

41.94 

83.94 

42.31 

94 

95 

85.39 

41.65 

85.20 

42.02 

85.02 

42.39 

84.83 

42.76 

95 

96 

86.28 

42.08 

86.10 

42.46 

85.91 

42.83 

85.73 

43.21 

96 

97 

87.18 

42.52 

87.00 

42.90 

86.81 

43.28 

86.62 

43.66 

97 

98 

88.08 

42.96 

87.89 

43.34 

87.70 

43.73 

87.51 

44.11 

98 

99 

88.98 

43.40 

88.79 

43.79 

88.60 

44.17 

88.40 

44.56 

99 

100 

89.88 

43.84 

89.69 

44.23 

89.49 

44.62 

89.30 

45.01 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

3 

64  Deg. 

63|  Deg. 

63|  Deg. 

63*  Deg. 

3 

56 


TRAVERSE    TABLE 


g 

27  Deg. 

27*  Deg. 

27£  Deg. 

27|  Deg. 

O 
5" 

£T 

I 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

1 

0.89 

0.45 

0.89 

0.46 

0.89 

0.46 

0.88 

0.47 

1 

8 

1.78 

0.91 

1.78 

0.92 

1.77 

0.92 

1.77 

0.93 

2 

3      2.67 

1.36 

2.67 

1.37 

2.66 

1.39 

2.65 

1.40 

3 

4 

3.56 

1.82 

3.56 

1.83 

3.55 

1.85 

3.54 

1.86 

4 

5 

4.45 

2.27 

4.45 

2.29 

4.44 

2.31 

4.42 

2.33 

5 

6 

5.35 

2.72 

5.33 

2.75 

5.32 

2.77 

5.31 

2.79 

6 

7 

6.24 

3.18 

6.22 

3.21 

6.21 

3.23 

6.19 

3.26 

7 

8 

7.13 

3.63 

7.11 

3.66 

7.10 

3.69 

7.08 

3.72 

8 

9 

8.02 

4.09 

8.00 

4.12 

7.98 

4.16 

7.96 

4.19 

9 

10 

8.91      4.54 

8.89 

4.58 

8.87 

4,62 

8.85 

4.66 

10 

11 

9.80 

4.99  ! 

9.78 

5.04 

9.76 

5.08 

9.73 

5.12 

11 

12 

10.69 

5.45 

10.67 

5.49 

10.64 

5.54 

10.62 

5.59 

12 

13 

1  1  .  58 

5.90 

11.56 

5.95 

11.53 

6.00 

11.50 

6.05 

13 

14 

12.47 

6.36 

12.45 

6.41 

12.42 

6.46 

12.39 

6.52 

14 

15 

13.37 

6.81 

13.34 

6.87 

13.31 

6.93 

13.27 

6.98 

15 

16 

14.26 

7.26 

14.22 

7.33 

14.19 

7.39 

14.16 

7.45 

16 

17 

15.15 

7.72 

15.11 

7.78 

15.08 

7.85 

15.04 

7.92 

17 

18 

16.04 

8.17 

16.00 

8.24 

15.97 

8.31 

15.93 

8.38 

18 

19 

16.93 

8.63 

16.89 

8.70 

16.85 

8.77 

16.81 

8.85 

19 

20 

17.82 

9.08 

17.78 

9.16 

17.74 

9.23 

17.70 

9.31 

20 

21 

18.71 

"  9  .  53 

18.67 

9.62  i 

18.63 

9.70 

18.58 

9.78 

21 

22 

19.60 

9.99 

19.56 

10.07 

19.51 

10.16 

19.47 

10.24 

22 

23 

20.49 

10.44 

20.45 

10.53 

20.40 

10.62 

20.35 

10.71 

23 

24 

21.38 

10.90 

21.34 

10.99 

21.29 

11.08 

21.24 

11.17 

24 

25 

22.2-8 

11.35 

22  .  23 

11.45 

22.18 

11.54 

22.12 

11.64 

25 

26 

23.17 

11.80 

23.11 

11.90 

23.06 

12.01 

23.01 

12.11 

26 

27 

24.06 

12.26 

24.00 

12.36 

23.95 

12.47 

23.89 

12.57 

27 

28 

24.95 

12.71 

24.89 

12.82 

24.84 

12.93 

24.78 

13.04 

28 

29 

25.84 

13.17 

25.78 

13.28 

25.72 

13.39 

25.66 

13.50 

29 

30 

26.73 

13.62 

26.67 

13.74 

26.61 

13.85 

26.55 

13.97 

30 

31 

27.62 

14.07 

27.56 

14.19 

27.50 

14.31 

27.43 

14.43 

31 

32 

28.51 

14.53 

28.45 

14.65 

28.38 

14.78 

28.32 

14.90 

32 

33 

29.40 

14.98 

29.34 

15.11 

29.27 

15.24 

29.20 

15.37 

33 

34 

30.29 

15.44 

30.23 

15.57 

30.16 

15.70 

30.09 

15.83 

34 

35 

31.19 

15.89 

31.12 

16.03 

31.05 

16.16 

30.97 

16.30 

35 

36 

32  .  08 

16.34 

32.00 

16.48 

31.93 

16.62 

31.86 

16.76 

36 

37 

32.97 

16.80 

32.89 

16.94 

32.82 

17.08 

32.74 

17.23 

37 

38 

33.86 

17.25 

33.78 

17.40 

33.71 

17.55 

33.63 

17.69 

38 

39 

34.75 

17.71 

34.67 

17.86 

34.59 

18.01 

34.51 

18.16 

39 

40 

3ft  .  64 

18.16 

35.56 

18.31 

35.48 

18.47 

35.40 

18.62 

40 

41 

36.53 

18.61 

36.45 

18.77 

36.37 

18.93 

36.28 

19.09 

41 

42 

37.42 

19.07 

37.34 

19.23 

37.25 

19.39 

37.17 

19.56 

42 

43 

38.31 

19.52 

38.23 

19.69 

38.14 

19.86 

38.05 

20.02 

43 

44 

39.20 

19.98 

39.12 

20.15 

39.03 

20.32 

38.94 

20.49 

44 

45 

40.10 

20.  £3 

40.01 

20.60 

39.92 

20.78 

39.82 

20  .  95 

45 

46 

40.99 

20.88 

40.89 

21.06 

40.80 

21.24 

40.71 

21.42 

46 

47 

41.88 

21.34 

41.78 

21.52 

41.69 

21.70 

41.59 

21.88 

47 

48 

42.77  121.79 

42.67 

21.98 

42.58 

22.16 

42.48 

22.35 

48 

49 

43.66 

22.25 

43.56 

22.44 

43.46 

22.63 

43.36 

22.82 

49 

50 

44.55 

22.70 

44.45 

22.89 

44.35 

23.09 

44.25 

23.28 

50 

I 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

§ 

* 

•5 

JS 

63  Deg. 

62|  Deg. 

62|  Deg. 

62*  Deg. 

ft 

TRAVERSE   TABLE. 


g 

27  Deg. 

27*  Deg. 

27£  Deg. 

27|  Deg. 

O 

5»> 

I 

| 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

51 

45.44 

23.15 

45.34 

23.35 

45.24 

23.55 

45.13 

~23~775~ 

51 

52 

46.33 

23.61 

46.23 

23.81 

•46.12 

24.01 

46.02 

24.21 

52 

53 

47.22 

24.06 

47.12 

24.27 

47.01 

24.47 

46.90 

24.68 

53 

54 

48.11 

24.52 

48.01 

24.73 

47.90 

24.93 

47.79 

25.14 

54 

55 

49.01 

24.97 

48.90 

25.18 

48.79 

25.40 

48.67 

25.61 

55 

56 

49.90 

25.42 

49.78 

25.64 

49.67 

25.86 

49.56 

26.07 

56 

57 

50.79 

25.88 

50.67 

28.10 

50.56 

26.32 

50.44 

26.54 

57 

58 

51.68 

26.33 

51.56 

26.56 

51.45 

26.78 

51.33 

27.01 

58 

59 

52.57 

26.79 

52.45 

27.01 

52.33 

27.24 

52.21 

27.47 

59 

60 

53.46 

27.24 

53.34 

27.47 

53.22 

27.70 

53.10 

27.94 

60 

61 

54.35 

27.69 

54.23 

27.93 

54.11 

28.17 

53.98 

28.40 

61 

62 

55.24 

28.15 

55.12 

28.39 

54.99 

28.63 

54.87 

28.87 

62 

63 

56.13 

28.60 

56.01 

28.85 

55.88 

29.09 

55.75 

29.33 

63 

64 

57.02 

29.06 

56.90 

29.30 

56.77 

29.55 

56.64 

29.80 

64 

65 

57.92 

29.51 

57.79 

29.76 

57.66 

30.01 

57.52 

30.26 

65 

66 

58.81 

29.96 

58.68 

30.22 

58.54 

30.48 

58.41 

30.73 

66 

67 

59  .  70 

30.42 

59.56 

30.68 

59.43 

30.94 

59.29 

31.20 

67 

68 

60.59 

30.87 

60.45 

31.14 

60.32 

31.40 

60.18 

31.66 

68 

69 

61.48 

31.33 

61.34 

31.59 

61.20 

31  .86 

61.06 

32.13 

69 

70 

62.37 

31.78 

62.23 

32.05 

62.09 

32.32 

61.95 

32.59 

70 

71 

63.26 

32.23 

63.12 

32.51 

62.98 

32.78 

62.83 

33.06 

71 

72 

64.15 

32.69 

64.01 

32  .  97 

63.86 

33.25 

63.72 

33  .  52 

72 

73 

65.04 

33.14 

64.90 

33.42 

64.75 

33.71 

64.60 

33.99 

73 

74 

65  .  93 

33.60 

65  .  79 

33.88 

65  .  64 

34.17 

65.49 

34.46 

74 

75 

66.83 

34.05 

66.68 

34.34 

66.53 

34.63 

66.37 

34.92 

75 

76 

67.72 

34.50 

67.57 

34.80 

67.41 

35.09 

67.26 

35.39 

76 

77 

68.61 

34.96 

68.45 

35.26 

68.30 

35.55 

68.14 

35.85 

77 

78 

69.50 

35.41 

69.34 

35.71 

69.19 

36.02  I!  69.03 

36.32 

78 

79 

70.39 

35.87 

70.23 

36.17 

70.07 

36.48 

69.91 

36.78 

79 

80 

71.28 

36.32 

71-12 

36.63 

70.96 

36.94 

70.80 

37.25 

80 

81 

72.17 

36.77 

72.01 

37.09 

71.85 

37.40 

71.68 

37.71 

81 

82 

73.06 

37.23 

72.90 

37.55 

72.73 

37.86 

72.57 

38.18 

82 

83 

73.95 

37.68 

73.79 

38.00 

73.62 

38.33 

73.45 

38.65 

83 

84 

74.84 

38.14 

74.68 

38.46 

74.51 

38.79 

74.34 

39.11 

84 

85 

75  .  74 

38  .  59 

75  .  57 

38.92 

75.40 

39.25 

75.22 

39.58 

85 

86 

76.63 

39.04 

76.46 

39.38 

76.28 

39.71 

76.11 

40.04 

86 

87 

77.52 

39.50 

77.34 

39.83 

77.17 

40.17 

76.99 

40.51 

87 

88 

78.41 

39.95 

78.23 

40.29 

78.06 

40.63 

TV.  88 

40.97 

88 

89 

79.30 

40.41 

79.12 

40  .  75 

78.94 

41.10 

78.76 

41.44 

89 

90 

80.19 

40.86 

80.01 

41.21 

79.83 

41.56 

79.65 

41.91 

90 

91 

81.08 

41.31 

80.90 

41.67 

80.72 

42.02 

80.53 

42.37 

91 

92 

81.97 

41.77 

81.79 

42.12 

81.60 

42.48 

81.42 

42.84 

'92 

93 

82.86 

42  .  22 

82.68 

42  .  58 

82.49 

42.94 

82.30 

43.30 

93 

94 

83  .  75 

42.68 

83.57 

43.04 

83.38 

43.40 

83.19 

43.77 

94 

95 

84.65 

43.13 

84.46 

43.50 

84.27 

43.87 

84.07 

44.23 

95 

96 

85  .  54 

43.58 

85.35 

43.96 

85.15 

44.33 

84.96 

44.70 

9f> 

97 

86.43 

44.04 

86.23 

44.41 

86.04 

44.79 

85.84 

45.16 

97 

98 

87.32 

44.49 

87.12 

44.87 

86.93 

45.25 

86.73 

45.63 

98 

99 

88.21 

44  .  95 

88.01 

45  .  33 

87.81 

45.71 

87.61 

46.10 

99 

100 

89.10 

45.40 

88.90 

45  .  79 

88.70 

46.17 

88.50 

46  .  56 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

ri 

.2 
Q 

63  Deg. 

62|  Deg. 

62£  Deg. 

62|  Deg. 

1 

TRAVERSE   TABLE. 


G 

28  Deg. 

284  Deg. 

28£  Deg. 

28|  Deg. 

O 

S- 

1 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1 

0.88 

0.47 

0.88 

0.47 

0.88 

0.48 

0.88 

0.48 

1 

2 

1.77 

0.94 

1.76 

0.95. 

1.76 

0.95 

1.75 

0.96 

2 

3 

2.65 

1.41 

2.64 

1.42 

2.64 

1.43 

2.63 

1.44 

3 

4 

3.53 

1.88 

3.52 

1.89 

3.52 

1.91 

3.51 

1.92 

4 

5 

4.41 

2.35 

4.40 

2.37 

4.39 

2.39 

4.38 

2.40 

5 

6 

5.30 

2.82 

5.29 

2.84 

5.27 

2.86 

5.26 

2.89 

6 

7 

6.18 

3.29 

6.17 

3.31 

6.15 

3.34 

6.14 

3.37 

7 

8 

7.06 

3.76 

7.05 

3.79 

7.03 

3.82 

7.01 

3.85 

8 

9 

7.95 

4.23 

7.93 

4.26 

7.91 

4.29 

7.89 

4.33 

9 

10 

8.83 

4.69 

8.81 

4.73 

8.79 

4.77 

8.77 

4.81 

10 

11 

9.71 

5.16 

9.69 

5.21 

9.67 

5.25 

9.64 

5.29 

11 

12 

10.60 

5.63 

10.57 

5.68 

10.55 

5.73 

10.52 

5.77 

12 

13 

11.48 

6.10 

11.45 

6.15 

11.42 

6.20 

11.40 

6.25 

13 

14 

12.36 

6.57 

12.33 

6.63 

12.30 

6.68 

12.27 

6.73 

14 

15 

13.24 

7.04 

13.21 

7.10 

13.18 

7.16 

13.15 

7.21 

15 

16 

14.13 

7.51 

14.09 

7.57 

14.06 

7.63 

14.03 

7.70 

16 

17 

15.01 

7.98 

14.98 

8.05 

14.94 

8.11 

14.90 

8.18 

17 

18 

15.89 

8.45 

15.86 

8.52 

15.82 

8.59 

15.78 

8.66 

18 

19 

16.78 

8.92 

16.74 

8.99 

16.70 

9.07 

16.66 

9.14 

19 

20 

17.66 

9.39 

17.62 

9.47 

17.58 

9.54 

17.53 

9.62 

20 

21 

18.54 

9.86 

18.50 

9.94 

18.46 

10.02  |  18.41 

10.10 

21 

22 

19.42 

10.33 

19.38 

10.41 

19.33 

10.50     19.29 

10.58 

22 

23 

20.31 

10.80 

20.26 

10.89 

20.21 

10.97    20.16 

11.06 

23 

24 

21.19 

11.27 

21.14 

11.36 

21.09 

11.45 

21.04 

11.54 

24 

25 

22.07 

1  1  .  74 

22.02 

11.83 

21.97 

11.93 

21.92 

12.02 

25 

26 

22.96 

12.21 

22  .  90 

12.31 

22.85 

12.41 

22.79 

12.51 

26 

27 

23.84 

12.68 

23.78 

12.78 

23  .  73 

12.88 

23.67 

12.99 

27 

28 

24.72 

13.15 

24.66 

13.25 

24.61 

13.36 

24.55 

13.47 

28 

29 

25.61 

13.61 

25.55 

13.73 

25.49 

13.84 

25.43 

13.95 

29 

30 

26.49 

14.08 

26.43 

14.20 

26.36 

14.31 

26.30 

14.43 

30 

31 

27.37 

14.55 

27.31 

14.67 

27.24 

14.79 

27.18 

14.91 

31 

32 

28.25 

15.02 

28.19 

15.15 

28.12 

15.27 

28.06 

15.39 

32 

33 

29.14 

15.49 

29.07 

15.62 

29.00 

15.75 

28  .  93 

15.87 

33 

34 

30.02 

15.96 

29.95 

16.09 

29.88 

16.22 

29.81 

16.35 

34 

35 

30  .  90 

16.43 

30.83 

16.57 

30.76 

16.70 

30.69 

16.83 

35 

36 

31.79 

16.90 

31.71 

17.04 

31.64 

17.18 

31.56 

17.32 

36 

37 

32.67 

17.37 

32,59 

17.51 

32.52 

17.65 

32.44 

17.80 

37 

38 

33.55 

17.-64 

33.47 

17.99 

33.39 

18.13 

33.32 

18.28 

38 

39 

34.43 

18.31 

34.35 

18.46 

34.27 

18.61 

34.19 

18.76 

39 

40 

35.32 

18.78 

35.24 

18.93 

35.15 

19.09 

35.07 

19.24 

40 

41 

36.20 

19.25 

36.12 

19.41 

36.03 

19.56 

35.95 

19.72 

41 

42 

37.08 

19.72 

37.00 

19.88 

36.91 

20.04 

36.82 

20.20 

42 

43 

37.97    20.19 

37.88 

20.35 

37.79 

20.52 

37.70 

20.68 

43 

44 

38.85 

20.66 

38.76 

20.83 

38.67 

20.99 

38.58 

21.16 

44 

45 

39.73 

21.13 

39.64 

21.30 

39.55 

21.47 

39.45 

21.64 

45 

40 

40.62 

21.60 

40.52 

21.77 

40.43 

21.95 

40.33 

22.13 

46 

47 

41.50 

22.07 

41.40 

22.25 

41.30 

22.43 

41.21 

22.61 

47 

48 

42.38 

22.53 

42.28 

22.72 

42.18 

22.90 

42.08 

23.09 

48 

49 

43.26 

23.00 

43.16 

23.19 

43.06 

23.38 

42.96 

23.57 

49 

50 

44.15 

23.47 

44.04 

23.67 

43.94 

23.86 

43.84 

24.05 

50 

o" 
1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

1 

1 

••3 

0 

62  Deg. 

6  If  Deg. 

61£  Deg. 

61i  Deg. 

•91 

Q 

• 

r 

TRAVERSE    TABLE. 


59 


o 

28  Deg. 

28i  Deg. 

28£  Deg. 

28|  Deg. 

O 

p 

1' 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

45.03 

23.94 

44.93 

24.14 

44.82 

24.34 

44.71 

24.53 

51 

52 

45.91 

24.41 

45.81 

24.61 

45.70 

24.81 

45.59 

25.01 

52- 

53 

46.80 

24.88 

46.69 

25.09 

.46  .  58 

25.29 

46.47 

25.49 

53 

54 

47.68 

25.35 

47.57 

25.56 

47.46 

25  .  77 

47.34 

25.97 

54 

55 

48.56 

25.82 

48.45 

26.03 

48  .  33 

26  .  24 

48.22 

26.45 

55 

56 

49.45 

26.29 

49.33 

26»51 

49.21 

26.72 

49.10 

26.94 

56 

57 

50.33 

26.76 

50.21 

26.98 

50.09 

27.20 

49.97 

27.42 

57 

58 

51.21 

27.23 

51.09 

27.45 

50.97 

27.68 

50.85 

27.90 

58 

59 

52.09 

27.70 

51.97 

27.93 

51.85 

28.15 

51.73 

28.38 

59 

60 

52.98 

28.17 

52.85 

28.40 

52  .  73 

28.63 

52  .  60 

28.86 

60 

61 

53.86 

28.64 

53.73 

28.87 

53.61 

29  .  1  1 

53.48 

29.34 

61 

62 

54.74 

29.11 

54.62 

29.35 

54.49 

29.58 

54.36 

29.82 

62 

63 

55  .  63 

29.58 

55.50 

29.82 

55.37 

30.06 

55.23 

30.30 

63 

64 

56.51 

30.05 

56.38 

30.29 

56.24 

30.54 

56.11 

30.78 

64 

65 

57.39 

30.52 

57.26 

30.77 

57.12 

31.02 

56.99 

31.26 

65 

66 

58.27 

30.99 

58.14 

31.24 

58.00 

31.49 

57.86 

31.75 

66 

67 

59.16 

31.45 

59  .  02 

31.71 

58.88 

31.97 

58.74 

32.23 

67 

68 

60.04 

31.92 

59.90 

32.19 

59.76 

32.45 

59  .  62 

32.71 

68 

69 

60.92 

32.39 

60.78 

32  .  66 

60.64 

32.92 

60.49 

33.19 

69 

70 

61.81 

32.85 

61.66 

33.13 

61.52 

33.40 

61.37 

33.67 

70 

71 

62.69 

33.33 

62  .  54 

33.61 

62.40 

33.88 

62.25 

34.15 

71 

72 

63.57 

33.80 

63.42 

34.08 

63.27 

34.36 

63.12 

34.63 

72 

73 

64.46 

34.27 

64.30 

34.55 

64.15 

34.83 

64.00 

35  .  1  1 

73 

74 

65.34 

34.74 

65.19 

35.03 

65.03 

35.31 

64.88 

35.59 

74 

75 

66.22 

35.21 

66.07 

35.50 

65.91 

35.79 

65  .  75 

36.07 

75 

76 

67.10 

35.68 

66.95 

35.97 

66  .  79 

36.26 

fi6.  63 

36.56 

76 

77 

67.99 

36.15 

67.83 

36.45 

67.67 

36.74 

67.51 

37.04 

77 

78 

68  .  87 

36.62 

68.71 

36.92 

68.55 

37.22 

68.38 

37.52 

78 

79 

69.75 

37.09 

69.59 

37.39 

69.43 

37.70 

69.26 

38.00 

79 

80 

70  .  64 

37.56 

70.47 

37.87 

70.31 

38.17 

70.14 

38.48 

80 

81 

71.52 

38.03 

71.35 

38.34 

71.18 

38  .  65 

71.01 

38.96 

81 

82 

72.40 

38.50 

72.23 

38.81 

72.06 

39.13 

71.89 

39.44 

82 

83 

73.28 

38.97 

73.11 

39.29 

72.94 

39  .  60 

72.77 

39  .  92 

83 

84 

74  .  ]  7 

39.44 

73.99 

39  .  76 

73.82 

40.08 

73.64 

40.40 

84 

85 

75.05 

39.91 

74.88 

40.23 

74.70 

40.56 

74.52 

40.88 

85 

86 

75  .  93 

40.37 

75.76 

40.71 

75  58 

41.04 

75.40 

41.36 

86 

87 

76.82 

40.84 

76.64 

41.18 

76.46 

41.51 

76.28 

41.85 

87 

88 

77.70 

41.31 

77.52 

41.65 

77.34 

41.99 

77.15 

42.33 

88 

89 

78.58 

41.78 

78.40 

42.13 

78.21 

42.47 

78.03 

42.81 

89 

90 

79.47 

42.25 

79.28 

42.60 

79.09 

42.94 

78.91 

43.29 

90 

91 

80.31T 

42.72 

80.16 

43.07 

79.97 

43.42 

79.78 

43.77 

91 

92 

81.23 

43.19 

81.04 

43.55 

80.85 

43.90 

80.66 

44.25 

92 

93 

82.11 

43.66 

81.92 

44.02 

81.73 

44.38 

81.54 

44.73 

93 

94 

83.00 

44.13 

82.80 

44.49 

82.61 

44.85 

82.41 

45.21 

94 

95 

83.88 

44.60 

83.68 

44.97 

83.49 

45.33 

83.29 

45.69 

95 

96 

84.76 

45.07 

84.57 

45.44 

84.37 

45.81 

84.17 

46.17 

96 

97 

85.65 

45.54 

85.45 

45.91 

85.25 

46.28 

85.04 

46.66 

97 

98 

86.53 

46.01 

86.33 

46.39 

86.12 

46.76 

85.92 

47.14 

98 

99 

87.41 

46.48 

87.21 

46.86 

87.00 

47.24 

86.80 

47.62 

99 

100 

88.29 

46.95 

88.09 

47.33 

87.88 

47.72 

87.67 

48.10 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

•3 

1 

Q 

62  Deg. 

6  If  Deg. 

61i  Deg. 

6H  Deg. 

3 

11 


60 


TRAVERSE    TOUSLE. 


i 

29  Deg. 

294  Deg. 

29i  Deg. 

29|  Deg. 

f 

§ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

i 

0.87 

0.48 

0.87 

0.49 

0.87 

0.491 

0.87 

0.50 

~T 

2 

1.75 

0.97 

1.74 

0.98 

1.74 

0.98 

1.74 

0.99 

2 

3 

2.62 

1.45 

2.62 

1.47 

2.61 

1.48 

2.60 

1.49 

3 

4 

3.50 

1.94 

3.49 

1.95 

3.48 

1.97 

3.47 

1.98 

4 

5 

4.37 

2.42 

4.36 

2.44 

4.35 

2.46 

4.34 

2.48 

5 

6 

5.25 

2.91 

5.23 

2.93 

5.22 

2.95 

5.21 

2.98 

6 

7 

6.12 

3.39 

6.11 

3.42 

6.09 

3.45 

6.08 

3.47 

7 

8 

7.00 

3.88 

6.98 

3.91 

6.96 

3.94 

6.95 

3.97 

8 

9 

7.87 

4.36 

7.85 

4.40 

7.83 

4.43 

7.81 

4.47 

9 

10 

8.75 

4.85 

8.72 

4.89 

8.70 

4,92 

8.68 

4.96 

10 

11 

9.62 

5.33 

9.60 

5.37 

9.57 

5.42 

9.55 

5.46 

11 

12 

10.50 

5.82 

10.47 

5.86 

10.44 

5.91 

10.42 

5.95 

12 

13 

11.37 

6.30 

11.34 

6.35 

11.31 

6.40 

11.29 

6.45 

13 

14 

12.24 

6.79 

12.21 

6.84 

12.18 

6.89 

12.15 

6.95 

14 

15 

13.12 

7.27 

13.09 

7.33 

13.06 

7.39 

13.02 

7.44 

15 

16 

13.99 

7.76 

13.96 

7.82 

13.93 

7.88 

13.89 

7.94 

16 

17 

1.4.87 

8.24 

14.83 

8.31 

14.80 

8.37 

14.76 

8.44 

17 

18 

15.74 

8.73 

15.70 

8.80 

15.67 

8.86 

15.63 

8.93 

18 

19 

16.62 

9.21 

16.58 

9.28 

16.54 

9.36 

16.50 

9.43 

19 

20 

17.49 

9.70 

17.45 

9.77 

17.41 

9.85 

17.36 

9.92 

20 

21 

18.37 

10.18 

18.32 

10.26 

18.28 

10.34 

18.23 

10.42 

21 

22 

19.24 

10.67 

19.19 

10.75 

19.15 

10.83 

19.10 

10.92 

22 

23 

20.12 

11.15 

20.07 

11.24 

20.02- 

11.33 

19.97 

11.41 

23 

24 

20.99 

11.64 

20.94 

11.73 

20.89 

11.82 

20.84 

11.91 

24 

25 

21.87 

12.12 

21.81 

12.22 

21.76 

12.31 

21.70 

12.41 

25 

26 

22.74 

12.60 

22.68 

12.70 

22.63 

12.80 

22.57 

12.90 

26 

27 

23.61 

13.09 

23.56 

13.19 

23.50 

13.30 

23.44 

13.40 

27 

28 

24.49 

13.57 

24.43 

13.68 

24.37 

13.79 

24.31 

13.89 

28 

29 

25.36 

14.06 

25.30 

14.17 

25.24 

14.28 

25.18 

14.39 

29 

30 

26.24 

14.54 

26.17 

14.66 

26.11 

14.77 

26.05 

14.89 

30 

31 

27.11 

15.03 

27.05 

15.15 

26.98 

15.27 

26.91 

15.38 

31 

32 

27.99 

15.51 

27.92 

15.64 

27.85 

15.76 

27.78 

15.88 

32 

33 

28.86 

16.00 

28.79 

16.12 

28.72 

16.25 

28.65 

16.38 

33 

34 

29.74 

16.48 

29.66 

16.61 

29.59 

16.74 

29.52 

16.87 

34 

35 

30.61 

16.97 

30.54 

17.10 

30.46 

17.23 

30.39 

17.37 

35 

36 

31.49 

17.45 

31.41 

17.59 

31.33 

17.73 

31.26 

17.86 

36 

37 

32.36 

17.94 

32.28 

18.08 

32.20 

18.22 

32.12 

18.36 

37 

38 

33.24 

18.42 

33.15 

18.57 

33.  07 

18.71 

32.99 

18.86 

38 

39 

34.11 

18.91 

34.03 

19.06 

33.94 

19.20 

33.86 

19.35 

39 

40 

34.98 

19.39 

34.90 

19.54 

34.81 

19.70 

34.73 

19.85 

40 

41 

35.86 

19.88 

35.77 

20.03 

35.68 

20.19 

35.60 

20.34 

41 

42 

36.73 

20.36 

36.64 

20.52 

36.55 

20.68 

36.46 

20.84 

42 

43 

37.61 

20.85 

37.52 

21.01 

37.43 

21.17 

37.33 

21.34 

43 

44 

38.48 

21.33 

38.39 

21.50 

38.30 

21.67 

38.20 

21.83 

44 

45 

39.36 

21.82 

39.26 

21.99 

39.17 

22.16 

39.07 

22.33 

45 

46 

40.23 

22.30 

40.13 

22.48 

40.04 

22.65 

39.94 

22.83 

46 

47 

41.11 

22.79 

41.01 

22.97 

40.91 

23.14 

40.81 

23.32 

47 

48 

41.98 

23.27 

41.88 

23.45 

41.78 

23.63 

41.67 

23.82 

48 

49 

42.86 

23.76 

42.75 

23.94 

42.65 

24.13 

42.54 

24.31 

49 

5_0_ 

43.73 

24.24 

43.62 

24.43 

43.52 

24.62 

43.41 

24.8! 

50 

& 
o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

a 
o 

c 

ei 

3 

61  Deg. 

60|  Deg. 

60^  Deg. 

604  Deg. 

"7 

3 

TRAVERSE    TABLE 


6i 


2 

on 

29  Deg. 

29i  Deg. 

29£  Deg. 

29|  Deg. 

I 

tance. 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

44.61 

24.73 

44,50 

24.92 

44.39 

25.11 

44.28 

25.31 

51 

52 

45.48 

25.21 

45.37 

25.41 

45.26 

25.61 

45.15 

25.80 

52 

53 

46.35 

25.69 

46.24 

25.90 

46.13 

26.10 

46.01 

26.30 

53 

54 

47.23 

26.18 

47.11 

26.39 

47.00 

26.59 

46.88 

26.80 

54 

55 

48.10 

26.66 

47.99 

26.87 

47.87 

27.08 

47.75 

27.29 

55 

56 

48.98 

27.15 

48.86 

27.36 

48.74 

27.58 

48.62 

27.79 

56 

57 

49.85 

^7.63 

49.73 

27.85 

49.61 

28.07 

49.49 

28.28 

57 

58 

50.73 

28.12 

50.60 

28.34 

50.48 

28.56 

50.36 

28.78 

58 

59 

51.60 

28.60 

51.48 

28.83 

51.35 

29.05 

51.22 

29.28 

59 

60 

52.48 

29.09 

52.35 

29.32 

52.22 

29.55 

52.09 

29.77 

60 

61 

53.35 

29  .  57 

53,22 

29.81 

53.09 

30.04 

52.96 

30.27 

61 

62 

54.23 

30.06 

54.09 

30.29 

53.96 

30.53 

53.83 

30.77 

62 

63 

55.10 

30.54 

54.97 

30.78 

54.83 

SI.  02 

54.70 

31.26 

63 

64 

55.98 

31.03 

55.84 

31.27 

55.70 

31.52 

55.56 

31.76 

64 

65 

56.85 

31.51 

56.71 

31.76 

56.57 

32.01 

56.43 

32.25 

65 

66 

57.72 

32.00 

57.58 

32.25 

57.44 

32.50 

57.30 

32.75 

66 

67 

58.60 

32.48 

58.46 

32.74 

58.31 

32.99 

58.17 

33.55 

67 

68 

59.47 

32.97 

59.33 

33.23 

59.18 

33.48 

59.04 

33.74 

68 

69 

60.35 

33.45 

60.20 

33.71 

60.05 

33.98 

59.91 

34.24 

69 

70 

61.22 

33,94 

61.07 

34.20 

60.92 

34.47 

60.77 

34.74 

70 

71 

62.10 

34.42 

61.95 

34.69 

61.80 

34.96 

61.64 

35.23 

71 

72 

62.97 

34.91 

62.82 

35.18 

62.67 

35,45 

62.51 

35.73 

72 

73 

63.85 

35.39 

63.69 

35.67 

63.54 

35.95 

63.38 

36.22 

73 

74 

64.72 

35.88 

64.56 

36.16 

64.41 

36.44 

64.25 

36.72 

74 

75 

65.60 

36.36 

65.44 

36.65 

65.28 

36.93 

65.11 

37.22 

75 

76 

66.47 

36.85 

66.31 

37.14 

66.15 

37.42 

65.98 

37.71 

76 

77 

67.35 

37.33 

67.18 

37.62 

67.02 

37.92 

66.85 

38.21 

77 

78 

68.22 

37.82 

68,05 

38.11 

67.89 

38.41 

67.72 

38.70 

78 

79 

69.09 

38.30 

68.93 

38.60 

68.76 

38.90 

68.59 

39.20 

79 

80 

69.97 

38,78 

69.80 

39.09 

69.63 

39.39 

69.46 

39.70 

80 

81 

70.84 

39.27 

70.67 

39.58 

70.50 

39.89 

70.32 

40.19 

81 

82 

71.72 

39.75 

71.54 

40.07 

71.37 

40.38 

71.19 

40.69 

82 

83 

72.59 

40.24 

72.42 

40.56 

72.24 

40.87 

72.06 

41.19 

83 

84 

73.47 

40.72 

73.29 

41.04 

73.11 

41.36 

72.93 

41.68 

84 

85 

74.34 

41.21 

74.16 

41.53 

73.98 

41.86 

73.80 

42.18 

85 

86 

75.22 

41.69 

75.03 

42.02 

74.85 

42.35 

74.67 

42.67 

86 

87 

76.09 

42.18 

75.91 

42.51 

75.72 

42.84 

75.53 

43.17 

87 

88 

76.97 

42.65 

76.78 

43.00 

76.59 

43.33 

76.40 

43.67 

88 

89 

77.84 

43.15 

77.65 

43.49 

77.46 

43.83 

77.27 

44.16 

89 

90 

78.72 

43.63 

78.52 

43.98 

78.33 

44.32 

78.14 

44.66 

90 

91 

79  .  59 

44.12 

79.40 

44.46 

79.20 

44.81 

79.01 

45.16 

91 

92 

80.46 

44.60 

80.27 

44.95 

80.07 

45.30 

79.87 

45.65 

92 

93 

81.34 

45.09 

81.14 

45.44 

80.94 

45.80 

80.74 

46.15 

93 

94 

82.21 

45.57 

82.01 

45.93 

81.81 

46.29 

81.61 

46.64 

94 

95 

83.09 

46.06 

82.89 

46,42 

82.68 

46.78 

82.48 

47.14 

95 

96 

83.96 

46.54 

83.76 

46.91 

83.55 

47.27 

83.35 

47.64 

96 

97 

84.84 

47.03 

84.63 

47.40 

84.42 

47.77 

84.22 

48.13 

97 

98 

85.71 

47.51 

85,50 

47.88 

85.29 

48.26 

85.08 

48.63 

98 

99 

86.59 

48.00 

86.38 

48.37 

86.17 

48.75 

85.95 

49.13 

99 

100 

87.46 

48.48 

87.  2f 

48.86 

87.04 

49.24 

86.82 

49.62 

100 

| 

Dep. 

Lat 

Dep 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

!'" 

Q 

61  Deg. 

60|  Deg. 

60|  Deg. 

60i  Deg. 

3 

i 

62 


TRAVERSE   TABLE. 


1 

30  Deg. 

30i  Deg. 

30|  Deg. 

30|  Deg. 

d 

sr 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

s 
o 

ra 

i 

0.87 

0.50 

0.86 

0.50 

(K86 

0.51 

0.86 

0.51 

1 

2 

1.73 

1.00 

1.73 

1.01 

1.72 

1.02 

1.72 

1.02 

2 

3 

2.60 

1.50 

2.59 

K51 

2.58 

1.52 

2.58 

1.53 

3 

4 

3.46 

2.00 

3.46 

2.02 

3.45 

2.03 

3.44 

2.05 

4 

5 

4.33 

2.50 

4.32 

2.52 

4.31 

2.54 

4.30 

2.56 

5 

6 

5.20 

3.00 

5.18 

3.02 

5.17 

3.05 

5.16 

3.07 

6 

7 

6.06 

3.50 

6.05 

3.53 

6.03 

3.55 

6.02 

3.58 

7 

8 

6.93 

4.00 

6.91 

4.03 

6.89 

4.06 

6.88 

4.09 

8 

9 

7.79 

4.50 

7.77 

4.53 

7.75 

4.57 

7.73 

4.60 

9 

10 

8.66 

5.00 

8.64 

5.04 

8.62 

5.08 

8.59 

5.11 

10 

11 

9.53 

5.50 

9.50 

5.54 

9.48 

5.58 

9.45 

5.62 

11 

12 

10.39 

6.00 

10.37 

6.05 

10.34 

6.09 

10.31 

6.14 

12 

13 

11.26 

6.50 

11.23 

6.55 

11.20 

6.60 

11.17 

6.65 

13 

14 

12.12 

7.00 

12.09 

7.05 

12.06 

7.11 

12.03 

7.16 

14 

15 

12.99 

7.50 

12.96 

7.56 

12.92 

7.61 

12.89 

7.67 

15 

16 

13.86 

8.00 

13.82 

8.06 

13.79 

8.12 

13.75 

8.18 

16 

17 

14.72 

8.50 

14.69 

8.56 

14.65 

8.63 

14.61 

8.69 

17 

18 

15.59 

9.00 

15.55 

9.07 

15.51 

9.14 

15.47 

9.20 

18 

19 

16.45 

9.50 

16.41 

9.57 

16.37 

9.64 

16.33 

9.71 

19 

20 

17.32 

10.00 

17.28 

10.08 

17.23 

10.15 

17.19 

10.23 

20 

21 

18.19 

10.50 

18.14 

10.58 

18.09 

10.66 

18.05 

10.74 

21 

22 

19.05 

11.00 

19.00 

11.08 

18.96 

11.17 

18.91 

11.25 

22 

23 

19.92 

11.50 

19.87 

11.59 

19.82 

11'.  67 

19.77 

11.76 

23 

24 

20.78 

12.00 

20.73 

12.09 

20.68 

12.18 

20.63 

12.27 

24 

25 

21.65 

12.50 

21.60 

12.59 

21.54 

12.69 

21.49 

12.78 

25 

26 

22.52 

13.00 

22.46 

13.10 

22.40 

13.20 

22.34 

13.29 

26 

27 

23.38 

13.50 

23.32 

13.60 

23.26 

13.70 

23.20 

13.80 

27 

28 

24.25 

14.00 

24.19 

14.11 

24.13 

14.21 

24.06 

14.32 

28 

29 

25.11 

14.50 

25.05 

14.61 

24.99 

14.72 

24.92 

14.83 

29 

30 

25.98 

15.00 

25.92 

15.11 

25.85 

15.23 

25  .  78 

15.34 

30 

31 

26.85 

15.50 

26.78 

15.62 

26.71 

15.73 

26.64 

15.85 

31 

32 

27.71 

16.00 

27.64 

16.12 

27.57 

16.24 

27.50 

16.36 

32 

33 

28.58 

16.50 

28.51 

16.62 

28.43 

16.75 

28.36 

16.87 

33 

34 

29.44 

17.00 

29.37 

17.13 

29.30 

17.26 

29.22 

17.38 

34 

35 

30.31 

17.50 

30.23 

17.63 

30.16 

17.76 

30  .  08 

17.90 

35 

36 

31.18 

18.00 

31.10 

18.14 

31.02 

18.27 

30.94 

18.41 

36 

37 

32.04 

18  30 

31.96 

18.64 

31.88 

18.78 

31.80 

18.92 

37 

38 

32.91 

19.00 

32.83 

19.14 

32.74 

19.29 

32.66 

19.43 

38 

39 

33.77 

19.50 

33.69 

19.65 

33.60 

19.79 

33.52 

19.94 

39 

40 

34.64 

20.00 

34.55 

20.15 

34.47 

20.30 

34.38 

20.45 

40 

41 

35.51 

20.50 

35.42 

20.65 

35.33 

20.81 

35.24 

20.96 

41 

42 

36.37 

21.00 

36.28 

21.16 

36.19 

21.32 

36.10 

21.47 

42 

43 

37.24 

21.50 

37.14 

21.66 

37.05 

21.82 

36.95 

21.99 

43 

44 

38.11 

22.00 

38.01 

22.17 

37.91 

22.33 

37.81 

22.50 

44 

45 

38.97 

22.50 

38.87 

22.67 

38  .  77 

22.84 

38.67 

23.01 

45 

46 

39.84 

23.00 

39.74 

23.17 

39.63 

23.35 

39.53 

23.52 

46 

47 

40.70 

23.50 

40.60 

23.68 

40.50 

23.85 

40.39 

24.03 

47 

48 

41.57 

24.00 

41.46 

24.18 

41.36 

24.36 

41.25 

24.54 

48 

49 

42.44 

24.50 

42.33 

24.68 

42.22 

24.87 

42  .  1  1 

25.05 

49 

50 

43.30 

25.00 

43.19 

25.19 

43.08 

25.38 

42  .  97 

25.56 

50 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

c 

Q 

60  Deg. 

59|  Deg. 

59}  Deg. 

59i  Deg. 

Q 

TRAVERSE    TABLE. 


63 


o 

x° 
p" 

30  Deg. 

30*  Deg. 

30i  Deg. 

30  ;  Deg. 

d 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

~51 

44.17 

25.50 

44.06 

25  .  69 

43.94 

25.88 

43.83 

26.08 

51 

52 

45.03 

26.00 

44.92 

26.20 

44.80 

26.39 

44.69 

26.59 

52 

53 

45.90 

26.50 

45.78 

26.70 

45.67 

26.90 

45.55 

27.10 

53 

54 

46  .  77 

27.00 

46.65 

27.20" 

46.53 

27.41 

46.41 

27.61 

54 

55 

47.63 

27.50 

47.51 

27.71 

47.39 

27.91 

47.27 

28.12 

55 

56 

48.50 

28.00 

48.37 

28.21 

48.25 

28.42 

48.13 

28.63 

56 

57 

49.36 

28.50 

49.24 

28.72 

49.11 

28.93 

48.99 

29.14 

57 

58 

50.23 

29.00 

50.10 

29.22 

49.97 

29.44 

49.85 

29.65 

58 

59 

51.10 

29.50 

50.97- 

29.72 

50.84 

29  .  94 

50.70 

30.17 

59 

80 

51.96 

3U.OO 

51.83 

30.23 

51.70 

30.45 

51.56 

30.68 

60 

61 

52  .  83 

30.50 

52.69 

30.73 

52.56 

30.96 

52.42 

31.19 

61 

62 

53.69 

31.00 

53.56 

31.23 

53.42 

31.47 

53.28 

31.70 

62 

63 

54.56 

31.50 

54.42 

31.74 

54.28 

31.97 

54.14 

32.21 

63 

64 

55.43 

32.00 

55.29 

32  .  24 

55.14 

32.48 

55.00 

32.72 

€4 

65 

56.29 

32.50 

56.15 

32.75 

56.01 

32.99 

55.86 

33.23 

65 

66 

57.16 

33.00 

57.01 

33.25 

56.87 

33.50 

56.72 

33.75 

66 

67 

58  .'02 

33  .  50 

57.88 

33.75 

07.73 

34.01 

57.58 

34.26 

67 

68 

58.89 

34.00 

58.74 

34.26 

58.59 

34.51 

58.44 

34.77 

68 

69 

59.76 

34.50 

59.60 

34.76 

59.45 

35.02 

59.30 

35.28 

69 

70 

60.62 

35.00 

60.47 

35.26 

60.31 

35.53 

60.16 

35.79 

70 

71 

61.49 

35.50 

61.33 

35.77 

61.18 

36.04 

61.02 

36.30 

71 

72 

62.35 

36.00 

62.20 

36.27 

62,04 

36.54 

61.88 

36.81 

72 

73 

63.22 

36.50 

63.06 

36.78 

62.90 

37.05 

62.74 

37.32 

73 

74 

64.09 

37.00 

63  .  92 

37.28 

63.76 

37.56 

63.60 

37.84 

74 

75 

64.95 

37.50 

64.79 

37.78 

64.62 

38.07 

64.46 

38.35 

75 

76 

65.82 

38.00 

65.65 

38.29 

65.48 

38.57 

65.31 

38.86 

76 

77 

66.68 

38,50 

66.52 

38  .  79 

66.35 

39.08 

66,17 

39.37 

77 

78 

67.55 

39.00 

67.38 

39.29 

67.21 

39.59 

67.03 

39.88 

78 

79 

68.42 

39.50 

68.24 

39.80 

68.07 

40.10 

67.89 

40.39 

79 

80 

69.28 

40.00 

69.11 

40.30 

68.93 

40.60 

68.75 

40.90 

80 

81 

70.15 

40.50 

69.97 

40.81 

69.79 

41.11 

69.61 

41.41 

81 

82 

71.01 

41.00 

70.83 

41.31 

70.65 

41.62 

70.47 

41.93 

82 

83 

71.88 

41.50 

71.70 

41.81 

71  .'52 

42.13 

71.33 

42.44 

83 

84 

72.75 

42.00 

72.56 

42.32 

72.38 

42.63 

72.19 

42.95 

84 

85 

73.61 

42.50 

73.43 

42.82 

73  .  24 

43.14 

73.05 

43.46 

85 

86 

74.48 

43.00 

74.29 

43.32 

74.10 

43.65 

73.91 

43.97 

86 

87 

75.34 

43.50 

75.15 

43.83 

74.96 

44.16 

74.77 

44.48 

87 

88 

76.21 

44.00 

76.02 

44.33 

75.82 

44.66 

75.63 

44.99 

88 

89 

77.08 

44.50 

76.88 

44.84 

76.68 

45.17 

76.49 

45.51 

89 

90 

77.94 

45.00 

77.75 

45.34! 

77.55 

45.68 

77.35 

46.02 

90 

91 

78.81 

45.50 

78.61 

45.84! 

78.41 

46.19 

78.21 

46.53 

91 

92 

79.67 

46.00 

79.47 

46.35 

79.27 

46.69 

79.07 

47.04 

92 

93 

80.54 

46.50 

80.34 

46.85 

80.13 

47.20 

79.92 

47.55 

93 

94 

81.41 

47.00 

81.20 

47.35 

80.99 

47.71 

80.78 

48.06 

94 

95 

82.27 

47.50 

82.06 

47.86  81.85 

48.22 

81.64 

48.57 

95 

96 

83.14 

48.00 

82.93 

48.36  82.72 

48.72 

82.50 

49.08 

96 

97 

84.00 

48.50 

83.79 

48.87  83.58 

49.23 

83.36 

49.60 

97 

98 

84.87 

49.00 

84.66 

49.37  i  84.44 

49  .  74 

84.22 

50.11 

98 

99 

85.74 

49.50 

85.52 

49.87  85.30 

50.25 

85.08 

50.62 

99 

100 

86.60 

50.00 

86.38 

50.38  86.16 

50.75 

85.94 

51.13 

100 

8 

Dep. 

La*. 

Dep. 

Lat.  jl  Dep. 

Lat. 

Dep. 

Lat. 

1 

rt 

1 

60  Deg. 

59f  Deg. 

59i  Deg. 

« 
59i  Deg. 

5 

11* 


64 


TRAVERSE   TABLE. 


M 

31  Deg. 

314  Deg. 

31  i  Deg. 

31  1  Deg. 

O 

& 

53' 
? 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 
O 

1 

0.86 

0.51 

0.85 

0.52 

0.85 

0.52 

0.85 

0.53 

1 

2 

1.71 

1.03 

1.71 

1.04 

1.71 

1.04 

1,70 

1,05 

2 

3 

2.57 

1.55 

2.56 

1.56 

2.56 

1.57 

2.55 

1.58 

3 

4 

3.43 

2.06 

3.42 

2.08 

3.41 

2.09 

3.40 

2.10 

4 

5 

4.29 

2.58 

4.27 

2.59 

4.26 

2.61 

4.25 

2.63 

5 

6 

5.14 

3.09 

5.13 

3.11 

5.12 

3.13 

5.10 

3.16 

6 

7 

6.00 

3.61 

5.98 

3.63 

5.97 

3.66 

5.95 

3.68 

7 

8 

6.86 

4.12 

6.84 

4.15 

6.82 

4.18 

6.80 

4.21 

8 

9 

7.71 

4.64 

7.69 

4.67 

7.67 

4.70 

7.65 

4.74 

9 

10 

8.57 

5.15 

8.55 

5.19 

8.53 

5.22 

8.50 

5.26 

10 

11 

9.43 

5.67 

9.40 

5.71 

9.38 

5.75 

9.35 

5.79 

11 

12 

10.29 

6.18 

10.26 

6.23 

10.23 

6.27 

10.20 

6.31 

12 

13 

11.14 

6.70 

11.11 

6.74 

11.08 

6.79 

11.05 

6.84 

13 

14 

12.00 

7.21 

11.97 

7.26 

11.94 

7.31 

11.90 

7.37 

14 

15 

12.86 

7.73 

12.82 

7.78 

12.79 

7.84 

12.76 

7.89 

15 

16 

13.71 

8.24 

13.68 

8,30 

13.64 

8.36 

13.61 

8.42 

16 

17 

14.57 

8.76 

14.53 

8.82 

14.49 

8.88 

14.46 

8.95 

17 

•18 

15.43 

9.27 

15.39 

9.34 

15.35 

9.40 

15.31 

9.47 

18 

19 

16.29 

9.79 

16.24 

9.86 

16.20 

9.93 

16.16 

10.00 

19 

20 

17.14 

10.30 

17.10 

10.38 

17.05 

10.45 

17.01 

10.52 

20 

21 

18.00 

10.82 

17.95 

10.89 

17.91 

10.97 

17.86 

11.05 

21 

22 

18.86 

11.33 

18.81 

11.41 

18.76 

11.49 

18.71 

1  1  .  58 

22 

23 

19.71 

11.85 

19.66 

11.93 

19.61 

12.02 

19.56 

12.10 

23 

24 

20.57 

12.36 

20.52 

12.45 

20.46 

12.54 

20,41 

12.63 

24 

25 

21.43 

12.88 

21.37 

12.97 

21.32 

13.06 

21.26 

13.16 

25 

26 

22.29 

13.39 

22.23 

13.49 

22.17 

13,58 

22.11 

13.68 

26 

27 

23.14 

13.91 

23.08 

14.01 

23.02 

14.11 

22.96 

14.21 

27 

28 

24.00 

14.42 

23.94 

14.53 

23.87 

14.63 

23.81 

14.73 

28 

29 

24.86 

14.94 

24.79 

15.04 

24.73 

15.15 

24.66 

1  5  .  26 

29 

30 

25.71 

15.45 

25.65 

15.56 

25.58 

15.67 

25.51 

15.79- 

30 

31 

26.57 

15.97 

26.50 

16.08 

26.43 

16.20 

26.36 

16.31 

31 

32 

27.43 

16.48 

27.36 

16.60 

27.28 

16.72 

27.21 

16.84 

32 

33 

28.29 

17.00 

28.21 

17,12 

28.14 

17.24 

28.06 

17.37 

33 

34 

29.14 

17.51 

29.07 

17.64 

28.99 

17.76 

28.91 

17.89 

3-1 

35 

30.00 

18,03 

29.92 

18.16 

29.84 

18.29 

29.76 

18.42 

35 

36 

30.  8G 

18.54 

30.78 

18.68 

30.70 

18.81 

30.61 

18.94 

36 

37 

31.72 

19.06 

31.63 

19.19 

31.55 

19.33 

31.46 

19.47 

37 

38 

32.57 

19.57 

32.49 

19.71 

32.40 

19.85 

32.31 

20.00 

38 

39 

33.43 

20.09 

33.34 

20.23 

33.25 

20.38 

33.16 

20.52 

39 

40 

34.29 

20.60 

34.20 

20.75 

34.11 

20.90 

34.01 

21.05 

40 

41 

35.14 

21.12 

35.05 

21.27 

34.96 

21.42 

34.86 

21.57 

41 

42 

36.00 

21.63 

35.91 

21.79 

35.81 

21.94 

35.71 

22.10 

42 

43 

36.86 

22.15 

36.76 

22.31 

36.66 

22.47 

36.57 

22.63 

43 

44 

37.72 

22.66 

37.62 

22.83 

37.52 

22.99 

37.42 

23.15 

44 

45 

38.57 

23.18 

38.47 

23.34 

38.37 

23.51 

38.27 

23.68 

45 

46 

39.43 

23.69 

39.33 

23.86 

39.22 

24.03 

39.12 

24.21 

46 

47 

40.29 

24.21 

40.18 

24.38 

40.07 

24.56 

39.97 

24.73 

47 

48 

41.14 

24.72 

41.04 

24.90 

40.93 

25.08 

40.82 

25.26 

48 

49 

42.00 

25  .  24 

41.89 

25.42 

41.78 

25.60 

41.67 

25.78 

49 

50 

42.86 

25.75 

42.75 

25.94 

42.63 

26.12 

42.52 

26.31 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

a 

Q 

59  Deg. 

58|  Deg. 

58i  Deg. 

58|  Deg. 

.2 

P 

TfiAVEfcSE   TAfiLE. 


c 

31  Deg. 

314  Deg. 

31^  Deg. 

31|  Deg. 

O 

p 

1 
P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

43.72 

26.27 

43.60 

26.46 

43.48 

26.65 

43.37 

26.84 

51 

52 

44.57 

26.78 

44.46 

26.98 

44.34 

27.17 

44.22 

27.36 

52 

53 

45.43 

27.30 

45.31 

27.49 

45.19 

27.69 

45.07 

27.89 

53 

54 

46.29 

27.81 

46.17 

28.01 

46.04 

28.21 

45.92 

28.42 

54 

55 

47.14 

28.33 

47.02 

28.53 

46.90 

28.74 

46.77 

28.94 

55 

56 

48.00 

28.84 

47.88 

29.05 

47.75 

29.26 

47.62 

29.47 

56 

57 

48.86 

29.36 

48  .  73 

29.57 

48.60 

29.78 

48.47 

29.99 

57 

58 

49  .  72 

29.87 

49.58 

30.09 

49.45 

30.30 

49.32 

30  .  52 

58 

59 

50  .  57 

30.39 

50.44 

30.61 

50.31 

30.83 

50.17 

31.05 

59 

60 

51.43 

30.90 

51.29 

31.13 

51.16 

31.35 

51.02 

31.57 

60 

61 

52.29 

31.42 

52.15 

31.65 

52.01 

31.87 

51.87 

32.10 

61 

62 

53.14 

31.93 

53  .  00 

32.16 

52.86 

32.39 

52.72 

32  .  63 

62 

63 

54.00 

32.45 

53.86 

32.68 

53.72 

32.92 

53.57 

33.15 

63 

64 

54.86 

32.96 

54.71 

33.20 

54.57 

33.44 

54.42 

33.68 

64 

65 

55.72 

33.48 

55.57 

33.72 

55.42 

33.96 

55.27 

34.20 

65 

66 

56.57 

33.99 

56.42 

34.24 

56  .  27 

34.48 

56.12 

34.73 

66 

67 

57.43 

34.51 

57.28 

34.76 

57.13 

35.01 

56.98 

35  .  26 

67 

68 

58.29 

35.02 

58.13 

35.28 

57.98 

35.53 

57.82 

35.78 

68 

69 

59.14 

35.54 

58.99 

35.80 

58.83 

36.05 

58  .  67 

36.31 

69 

70 

60.00 

36.05 

59.84 

36.31 

59.68 

36.57 

59  .  52 

36.83 

70 

71 

60.86 

36.57 

60.70 

36.83 

60.54 

37.10 

60.37 

37.36 

71 

72 

61.72 

37.08 

61.55 

37.35 

61.39 

37.62 

61.23 

37.89 

72 

73 

62.57 

37.60 

62.41 

37.87 

62.24 

38.14 

62.08 

38.41 

73 

74 

63.43 

38.11 

63.26 

38.39 

63.10 

38  .  66 

62.93 

38.94 

74 

75 

64.29 

38.63 

64.12 

38.91 

63.95 

39.19 

63.78 

39.47 

75 

76 

65.14 

39.14 

64.97 

39.43 

64.80 

39.71 

64.63 

39.99 

76 

77 

66.00 

39.66 

65.83 

39.95 

65.65 

40.23 

65.48 

40.52 

77 

78 

66,86 

40.17 

66.68 

40.46 

66.51 

40  .  75 

66.33 

41.04 

78 

79 

67.72 

40.69 

67.54 

40  .  98 

67.36 

41.28 

67.18 

41.57 

79 

80 

G8  .  57 

41.20 

68  .  39 

41.50 

68.21 

41.80 

38.03 

42.10 

80 

'81 

69.43  41.72 

69.25 

42  .  02 

69  .  06 

42.32 

68.88 

42.62 

81 

82 

70.29 

42.23 

70.10 

42.54 

69.92 

42.84 

69.73 

43.15 

82, 

83 

71.14 

42.75 

70.96 

43.06 

70  .  77 

43.37 

70.58 

43.68 

83 

84 

72.00 

43  .  26 

71.81 

43.58 

71.62 

43.89 

71.43 

44.20 

84 

85 

72.86 

43  .  78 

72.67 

44.10 

72.47 

44.41 

72  .  28 

44  .  73 

85 

86 

73.72 

44.29 

73.52 

44.61 

73.33 

44.93 

73.13 

45.25 

86 

87 

74.57 

44.81 

74.38 

45.13 

74.18 

45.46 

73.98 

45.78 

87 

88 

75.43 

45.32 

75.23 

45.65 

75.03 

45  .  98 

74.83 

46.31 

88 

89 

76.29 

45.84 

76.09 

46.17 

75.88 

46.50 

75.68 

46.83 

89 

90 

77.15 

46.35 

76.94 

46.69 

76  .  74 

47.02 

76  .  53 

47  .  36 

90 

91 

78.00 

46.87 

77.80 

47.21 

77.59 

47.55 

77.38 

47.89 

91 

92 

78.86 

47.38 

78.65 

47.73 

78.44 

48.07 

78.23 

48.41 

92 

93 

79.72 

47.90 

79.51 

48.25 

79.30 

48.59 

79.08 

48.94 

93 

94 

80.57 

48.41 

80.36 

48.76 

80.15 

49.11 

79  .  93 

49.47 

94 

95 

81.43 

48.93 

81.22 

49  .  28 

81.00 

49.64 

80.78 

49.99 

95 

96 

82.29 

49.44 

82.07 

49.80 

81.85 

50.16 

81.63 

50.52 

96 

97 

83.15 

49.96 

82.93 

50.32 

82.71 

50.68 

82.48 

5!.  04 

97 

98 

84.00 

50.47 

83  .  78 

50.84 

83.56 

51.20 

83,33 

51  .57 

98 

99 

84.86 

50.99 

84.64 

51.36 

84.41 

51.73 

84.18 

52.10 

99 

100 

85  .  72 

51.50 

85.49 

51.88 

85.26 

52.25 

85.04 

52.62 

100 

8 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

8 

d 

fl 

to 

p 

59  Deg. 

58|  Deg. 

58£  Deg. 

58J  Deg. 

Q 

66 


TRAVERSE    TABLE. 


o 
5 

32  Deg. 

32i  Deg. 

32£  Deg. 

32|  Deg. 

q 

55' 

P 

Lat. 

Dep. 

,  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.85 

0.53 

0.85 

0.53 

0.84 

0.54 

0.84 

0.54 

i 

2 

1.70 

1.06 

1.69 

1.07 

1.69 

1.07 

1.68 

1.08 

2 

3 

2.54 

1.59 

2.54 

1.60 

2.53 

1.61 

2.52 

1.62 

3 

4 

3.39 

2.12 

3.38 

2.13 

3.3~ 

2.15 

3.36 

2.16 

4 

5 

4.24 

2.65 

4.23 

2.67 

4.22 

2.69 

4.21 

2.70 

5 

6 

5.09 

3.18 

5.07 

3.20 

5.06 

3.22 

5.05 

3.25 

6 

7 

5.94 

3.71 

5.92 

3.74 

5.90 

3.76 

5.89 

3.  79 

7 

8 

6.78 

4.24 

6.77 

4.27 

6.75 

4.30 

6.73 

4.33 

8 

9 

7.63 

4.77 

7.61 

4.80 

7.59 

4.84 

7.57 

4.87 

9 

10 

8.48 

5.30 

8.46 

5.34 

8.43 

5.37 

8.41 

5.41 

10 

11 

9.33 

5.83 

9.30 

5.87 

9.28 

5.91 

9.25 

5.95 

11 

12 

10.18 

6.36 

10.15 

6.40 

10.12 

6.45 

10.09 

6.49 

12 

13 

11.02 

G.89 

10.99 

6.94 

10.96 

6.98 

10.93 

7.03 

13 

14 

11.87 

7.42 

11.84 

7.47 

11.81 

7.52 

11.77 

7.57 

14 

15 

12.72 

7.95 

12.69 

8.00 

12.65 

8.06 

12.62 

8.11 

15 

16 

13.57 

8.48 

13.53 

8.54 

13.49 

8.60 

13.46 

8.66 

16 

17 

14.42 

9.01 

14.38 

9.07 

14.34 

9.13 

14.30 

9.20 

17 

18 

15.26 

9.54 

15.22 

9.61 

15.18 

9.67 

15.14 

9.74 

18 

19 

16.11 

10.07 

16.07 

10.14 

16.02 

10.21 

15.98 

10.28 

19 

20 

16.96 

10.60 

16.91 

10.67 

16.87 

10.75 

16.82 

10.82 

20 

21 

17.81 

11.13 

17.76 

11.21 

17.71 

11.28 

17.66 

1  1  .  36 

21 

22 

18.66 

11.66 

18.61 

11.74 

18.55 

11.82 

18.50 

11.90 

22 

23  !  19.51 

12.19 

19.45 

12,27  !  19.40 

12.36 

19.34 

12.44 

23 

24 

20.35 

12.72 

20.30 

12.81 

20.24 

12.90 

20.18 

12.98 

24 

25 

21.20 

13.25 

21.14 

13.34 

21.08 

13.43 

21.03 

13.52 

25 

26 

22.05 

13.78 

21.99 

13.87 

21.93 

13.97 

21.87 

14.07 

26 

27 

22.90 

14.31 

22.83 

14.41 

22.77 

14.51 

22.71 

14.61 

27 

28 

23  .  75 

14.84 

23.68 

14.94 

23.61 

15.04 

23.55 

15.15 

28 

29 

24.59 

15.37 

24.53 

15.47 

24.46 

15.58 

24.39 

15i69 

29 

30 

25.44 

15.90 

25.37 

16.01 

25  .  30 

16.12 

25  .  23 

16.23 

30 

31  |26.29 

16.43 

26.22 

16.54 

26.15 

16.66 

26.07 

16.77 

81 

32 

27.14 

16.96 

27.06 

17.08 

26.99 

17.19 

26.91 

17.31 

32 

'  33 

27.99 

17.49 

27.91 

17.61 

27.83 

17.73 

27.75 

17.85 

33 

34 

28.83 

18.02 

28  .  75 

18.14 

28.68 

18.27 

28  .  60 

18.39 

34 

35 

29  .  68 

18.55 

29.60 

18.68 

29.52 

18.81 

29.44 

18.93 

35 

36 

30  .  53 

19.08 

30.45 

19.21 

30.36 

19.34 

30  .  28 

19.48 

30 

37 

31.38 

19.61 

31.29 

19.74 

31.21 

19.88 

31.12 

20.05 

37 

38 

32.23 

20.14 

32.14 

20.28 

32.05 

20.42 

31.96 

20.56 

38 

39 

33.07 

20.67  [32.98 

20.81 

32.89 

20.95 

32.80 

21.10 

39 

40 

33.92 

21.20 

33.83 

21.34 

33.74 

21.49 

33  .  64 

21.64 

40 

41 

34.77 

21.73 

34.67 

21.88 

34.58 

22.03 

34.48 

22.18 

41 

42 

35.62 

22.26 

35.52 

22.41 

35.42 

22.57 

35  .  32 

22  .  72 

42 

43 

36.47 

22.79 

36  .  37 

22.95 

36.27 

23.10 

36.16 

23.26 

43 

44137.31 

23.32 

37.21 

23.48 

37.11 

23.64 

37.01 

23.80 

44 

45 

38.16 

23.85 

38.06 

24.01 

37.95 

24.18 

37.85 

24.34 

45 

46 

39.01 

24.38 

38.90 

24.55 

38.80 

24.72 

38.69 

24.88 

46 

47 

3J.86 

24.91 

39.75 

25.08 

39.64 

25.25 

39.53 

25.43 

47 

48 

40.71 

25.44 

40.59 

25.61 

40.48 

25.79 

40.37 

25  .  97 

48 

49 

41.55 

25.97 

41.44 

26.15 

41.33 

26.33 

41.21 

26.51 

49 

50 

42.40 

26.50 

42.29 

26  .  68 

42.17 

26.86 

42.05 

27.05 

50 

QJ 
| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

§ 

Jj 

.      , 

1 

"to 

'JO 

Q 

58  Deg. 

57|  Deg. 

57£  Deg. 

57}  Deg. 

b 

TRAVERSE    TABLE. 


67 


j? 

32  Deg. 

324  Deg. 

32i  Deg. 

32|  Deg. 

O 

I 

c* 

3 
o 
a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

CD 

~51 

43.25 

27.03 

43.13 

27.21 

43.01 

"2T.40" 

42.89 

27.59 

51 

52 

44.10 

27.56 

43.98 

27.75 

43.86 

27.94 

43  .  73 

28.13 

52 

53 

44.95 

28.09 

44.82 

28.28 

44.70 

28.48 

44.58 

28.67 

53 

54 

45.79 

28.62 

45.67 

28.82 

45.54 

29.01 

45.42 

29.21 

54 

55 

46.64 

29.15 

46.51 

29,35 

46  .  39 

29.55 

46.26 

29  .  75 

55 

56 

47.49 

29.68 

47.36 

29.88 

47.23 

30.09 

47.10 

30  .  29 

56 

57 

48.34 

30.21 

48.21 

30.42 

48.07 

30.63 

47.94 

30.84 

57 

58 

49.19 

30.74 

49  .  05 

30.95 

48  .  92 

31.16 

48.78 

31.38 

58 

59 

50.03 

31.27 

49.90 

31.48 

49.76 

31.70 

49.62 

31.92 

59 

60 

50.88 

31.80 

50.74 

32.02 

50  .  60 

32.24 

50.46 

32.46 

60 

61 

51.73 

32.33 

51.59 

32.55 

51.45 

32  .  78 

51.30 

33.00 

61 

62 

52.58 

32.85 

52.44 

33.08 

52.29 

33.31 

52.14 

33.54 

62 

63 

53.43 

33.38 

53.28 

33.62 

53.13 

33.85 

52  .  99 

34.08 

63 

64 

54.28 

33.91 

54.13 

34.15 

53.98 

34.39 

53.83 

34.62 

64 

65 

55.12 

34.44 

54.97 

34.68 

54.82 

34  .  92 

54.67 

35.16 

65 

66 

55.97 

34.97 

55.82 

35.22 

55  .  66 

35.46 

55.51 

35  .  70 

66 

67 

56.82 

35.50 

56.66 

35.75 

56.51 

36.00 

56  .  35 

36.25 

67 

68 

57.67 

36.03 

57.51 

36  .  29 

57.35 

36.54 

57.19 

36.79 

68 

69 

58.52 

36.56 

58.36 

36.82 

58.19 

37.07 

58.03 

37.33 

69 

70 

59.36 

37.09 

59.20 

37.35 

59.04 

37.61 

58.87 

37.87 

70 

71 

60.21 

37.62 

60.05 

37.89 

59.88 

38.15 

59.71 

38.41 

71 

72 

61.06 

38.15 

60.89 

38.42 

60.72 

38.69 

60  .  55 

38.95 

72 

73 

61.91 

38.68 

61.74 

38  .  95 

61.57 

39.22 

61.40 

39.49 

73 

74 

62.76 

39.21 

62.58 

39.49 

62.41 

39  .  76 

62.24 

40.03 

74 

7-5 

63.60 

39  .  74 

63.43 

40.02 

63.25 

40  .  30 

63.  OS 

40.57 

75 

76 

64.45 

40.27 

64.28 

40.55 

64.10 

40.83 

63.92 

41.11 

76 

77 

65.30 

40.80 

65.12 

41.09 

64.94 

41.37 

64.76 

41.65 

77 

78 

66.15 

41.33 

65.97 

41.62 

65.78 

41.91 

65  .  60 

42.20 

78 

79 

67.00 

41.86 

66.81 

42.16 

66  .  63 

42.45 

66.44 

42.74 

79 

80 

67.84 

42.39 

67.66 

42  .  69 

67.47  i  42.98 

67.28 

43.28 

80 

81 

68.69 

42  .  92 

68.50 

43.22 

68.31 

43.52 

68.12 

43.82 

81 

82 

69.54 

43.45 

69.35 

4-3  .  76 

69.16 

44.06 

68.97 

44.36 

82 

S3 

70.39 

43.98 

70.20 

44.29 

70  .  00 

44.60 

69.81 

44.90 

83 

84 

71.24 

44.51 

71.04 

44.82 

70.84 

45.13 

70.65 

45.44 

84 

85 

72.08 

45.04 

71.89 

45.36 

71.69 

45.67 

71.49 

45  .  98 

85 

86 

72.93 

45.57 

72.73 

45  .  89 

72.53 

46.21 

72.33 

46  .  52 

86 

87 

73.78 

46.10 

73  .  58 

46.42 

73.38 

46.75 

73.17 

47.06 

87 

88 

74.63 

46.63 

74.42 

46  .  96 

74.22 

47.28 

74.01 

47.61 

88 

89 

75.48 

47.16 

75.27 

47.49 

75.06 

47.82 

74.85 

48.15 

89 

90 

76.32 

47.69 

76.12 

48.03 

75.91 

48.36 

75  .  69 

48.69 

90 

91  (77.17 

48.22 

76.96 

48.56 

76.75 

48.89 

76.53 

49  .  23 

91 

92  78.02 

48.75 

77.81 

49.09 

77.59 

49.43 

77.38 

49  77 

92 

93!  78.87 

49.28 

78  .  65 

49.63 

78.44 

49.97 

78.22 

50.31 

93 

94  79.72 

49.81 

79.50 

50.16 

79.28 

50.51 

79.06 

50.85 

94 

95 

80.56 

50.34 

80.34 

50.69 

80.12 

51.04 

79.90 

51.39 

95 

96 

81.41 

50.87 

81.19 

51.23 

80.97 

51.58 

80.74 

51.93 

96 

97 

82.26 

51.40 

82.04 

51.76 

81.81 

52.12 

81.58 

52.47 

97 

98 

83.11 

51.93 

82.88 

52.29 

82.65 

52.66 

82.42 

53.02 

98 

99  ;  83.96 

52.46 

83.73 

52.83 

83.50 

53.19 

83.26 

53.56 

99 

100 

84.80 

52.99 

84.57 

53.36 

84.34 

53.73 

84.10 

54.10 

100 

£3 
d 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

| 

09 

g 
b 

58  Deg. 

57!  Deg. 

57i  Deg. 

574  Deg. 

.3 
Q 

68 


TRAVERSE    TABLE. 


o 

33  Deg. 

334  Deg. 

33i  Deg. 

331  Deg. 

C 

02 

¥ 

a 

a 
o 

CD 

Lat.  |  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

~~7 

0.84 

0.54 

0.84 

0.55 

0.83 

0.55 

0.83 

0.56 

i 

2 

1.68 

1.09 

1.67 

1.10 

1.67 

1.10 

1.66 

1.11 

2 

3 

2.52 

1.63 

2.51 

1.64 

2.50 

1.66 

2.49 

1.67 

3 

4 

3.35 

2.18 

3.35 

2.19 

3.34 

2.21 

3.33 

2.22 

4 

5 

4.19 

2.72 

4.18 

2.74 

4.17 

2.76 

4.16 

2.78 

5 

6 

5.03 

3.27 

5  .  02 

3.29 

5.00 

3.31 

4.99 

3.33 

6 

7 

5.87 

3.81 

5.85 

3.84 

5.84 

3.86 

5.82 

3.89 

7 

8 

6.71 

4.36 

6.69 

4.39 

6.67 

4.42 

6.65 

4.44 

8 

9 

7.55 

4.90 

7.53 

4.93 

7.50 

4.97 

7.48 

5.00 

9 

10 

8.39 

5.45 

8.36 

5.48 

8.34 

5  .  52 

8.31 

5.56 

10 

11 

9.23 

5.99 

9.20 

6.03 

9.17 

6.07 

9.15 

6.11 

11 

12 

10.06 

6.54 

10.04 

6.58 

10.01 

6.62 

9.98 

6.67 

12 

13 

10.90 

7.08 

10.87 

7.13 

10.84 

7.18 

10.81 

7.22 

13 

14 

11.74 

7.62 

11.71 

7.68 

11.67 

7.73 

11.64 

7.78 

14 

15 

12.58 

8.17 

12.54 

8.22 

12.51 

8.28 

12.47 

8.33 

15 

16 

13.42 

8.71 

13.38 

8.77 

13.34 

8.83 

13.30 

8.89 

16 

17 

14.26 

9.26 

14.22 

9.32 

14.18 

9.38 

14.13 

9.44 

17 

18 

15.10 

9.80 

15.05 

9.87 

15.01 

9.93 

14.97 

10.00 

18 

19 

15.93 

10.35 

15.89 

10.42 

15.84 

10.49 

15.80!  10.56 

19 

20 

16.77 

10.89 

16.73 

10.97 

16.68 

1  1  .  04 

16.631  11.11 

20 

21 

17.61 

11.44 

17.56 

11.51 

17.51 

11.59 

17.46    11.67 

21 

22 

18.45 

11.98 

18.40 

12.06 

18.35 

12.14 

18.29 

12.22 

22 

23 

19.29 

12.53 

19.23 

12.61 

19.18 

12.69 

19.12 

12.78 

23 

24 

20.13 

13.07 

20.07 

13.16 

20.01 

13.25 

19.96 

13.33 

24 

25 

20  .  97 

13.62 

20.91 

13.71 

20.85 

13.80 

20.79 

13.89 

25 

26 

21.81 

14.16 

21.74 

14.26 

21.68 

14.35 

21.62 

14.44 

26 

27 

22.64 

14.71 

22.58 

14.80 

22.51 

14.90 

22.45 

15.00 

27 

28 

23.48 

15.25 

23.42 

15.35 

23.35 

15.45 

23.28 

15.56 

28 

29 

24.32 

15.79 

24.25 

15.90 

24.18 

16.01 

24.11 

16.11 

29 

30 

25.16 

16.34 

25.09 

16.45 

25.02 

16.56 

24.94 

16.67 

30 

31 

26.00 

16.88 

25.92 

17.00 

25.85 

17.11 

25.78 

17.22 

31 

32 

26  .  84 

17.43 

26.76 

17.55 

26.68 

17.66 

26.61 

17.78 

32 

33 

27.63 

17.97 

27.60 

18.09 

27.52 

18.21 

27.44 

18.33 

33 

34 

23.51 

18.52 

28.43 

18.64 

28.35 

18.77 

28.27 

18.89 

34 

35 

29  .  35 

19.06 

29  .  27 

19.19 

29.19 

19.32 

29.10 

19.44 

35 

36 

30.19 

19.61 

30  .  1  1 

19.74 

30.02 

19.87 

29.93 

20.00 

36 

37 

3  1  .  03 

20.15 

30.94 

20.29 

30.85 

20.42 

30.76 

20.56 

37 

38 

31.87 

20.70 

31.78 

20.84 

31.69 

20.97 

31.60 

21.11 

38 

39 

32  71 

21.24 

32  .  82 

21.38 

32.52 

21.53 

32.43 

21.67 

39 

40 

33  .  55 

21.79 

33.45 

21.93 

33.36 

22.08 

33.26 

22.22 

40 

41 

31  .  39 

22.33 

34.29 

22.48 

34.19 

22.63 

34.09 

22.78 

41 

42 

35.22 

22.87 

35.12 

23.03 

35.02 

23.18 

34.92 

23.33 

42 

43 

3o  .  06 

23.42 

35.96 

23.58 

35.86 

23.73 

35.75 

23.89 

43 

44 

33.90 

23  .  96 

36.80 

24.12 

36.69 

24.29 

36.58 

24.45 

44 

45 

37.74 

24.51 

37.63 

24.67 

37.52 

24.84 

37.42 

25.00 

45 

46 

33  .  58 

25.05 

38.47 

25.22 

38.36 

25.39 

38.25 

25.56 

46 

47 

39.42 

25.60 

39.31 

25.77 

39.19 

25.94 

39.08 

26.11 

47 

48 

40.23 

26.14 

40.14 

26.32 

40.03 

23.49 

39.91 

26.67 

48 

49 

41.09 

26.69 

40.98 

26.87 

40.86 

27.04 

40.74 

27.22 

49 

50 

41.93 

27.23 

41.81 

27.41 

41.69 

27.60 

41.57 

27.78 

50 

1 

Dep 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

to 

o 

rt 

s 

57  Deg. 

56|  Deg. 

56i  Deg. 

56i  Deg. 

Q 

TRAVEKSE   TABLE. 


69 


4 

5? 

33  Deg. 

33i  Deg. 

33^  Deg. 

33J  Deg. 

O 
5' 

s 

Lat. 

tance. 

Lat. 

Dep. 

Dep. 

Lat. 

Dep 

Lat. 

Dep. 

51 

42.77 

27.78 

42.65 

27.98 

42.53 

28.  ill 

42.40 

28.33 

51 

52 

43.61 

28.32 

43.49 

28.51 

43.36 

28-70 

43.24 

28.89 

52 

53 

44.45 

28.87 

44.32 

29.06 

44.20 

29.25 

44.07 

29.45 

53 

54 

45.29 

29.41 

45.16 

29.61 

45.03 

29.80 

44.90 

30.00 

54 

55 

46.13 

29.96 

46.00 

30.16 

45.86 

30.36 

45.73 

30.56 

55 

56 

46.97 

30.50 

46.83 

30.70 

46.70 

30.91 

40.56 

31.11 

56 

57 

47.80 

31.04 

47.67 

31.25 

47.53 

31.46 

47.39 

31.67 

57 

58 

48.64 

31.59 

48.50 

31.80 

48.37 

32.01 

48.23 

82.22 

58 

59 

49.48 

32.13 

49.34 

32.35 

49.20 

32.50 

49.06 

32.78 

59 

60 

50.32 

32.68 

50.18 

32.90 

50.03 

33.12 

49.89 

33.33 

60 

"61 

51.16 

33.22 

51.01 

33.45 

50.87 

33.67 

50  .  72 

33.89 

61 

62 

52.00 

33.77 

51.85 

33  .  99 

51.70 

34.22 

51.55 

34.45 

02 

63 

52.84 

34.31 

52.69 

34.54 

52.53 

34.77 

52.38 

35.00 

63 

64 

53.67 

34.86 

53.52 

35.09 

53.37 

35.32 

53.21 

35.56 

64 

65 

54.51 

35.40 

54.36 

35.64 

54.20 

35.88 

54.05 

36.11 

65 

66 

55  .  35 

35.95 

55.19 

36.19 

55.04 

36.43 

54.88 

36.07 

GO 

07 

56.19 

36.49 

56.03 

36  .  74 

55.87 

36.98 

55.71 

37.22 

07 

08 

57.03 

37.04 

56.87 

37.28 

56  .  70 

37.53 

56.54 

37  .  78 

08 

69 

57.87 

37.58 

57  .  70 

37.83 

57.54 

38.08 

57.37 

38.33 

09 

70 

58.71 

38  .  1  2 

58  .  54 

38.38 

58.37 

38.64 

58.20 

38.89  1   70 

71 

59.55 

38.67 

59.38 

38.93 

59.21 

39.19 

59.03 

39.45 

71 

72. 

60.38 

39.21 

60.21 

39.48 

60.04 

39.74     59.87 

40.00 

72 

73 

61.22 

39.76 

61.05 

40.03 

60.87 

40.29  i 

60.70 

40.56 

73 

74 

62.06 

40.30 

61.89 

40.57 

61.71 

40.84 

61.53 

41.11 

74 

75 

62.90 

40.85 

62  .  72 

41.12 

62.54 

41.40 

62.36 

41.67 

75 

76 

6'3  .  74 

41.39 

03.56 

41.67 

63.38 

41.95 

63.19  142.22 

70 

77 

64.58 

41.94 

64.39 

42.22 

64.21 

42  .  50 

64.02 

42.78 

77 

78 

65.42 

42.48 

65.23 

42.77 

05.04 

43.05 

64.85 

43.33 

78 

79 

66.25 

43.03 

66.07 

43.32 

05.88 

43  .  60 

65.69 

43.89 

79 

80 

67.09 

43  .  57 

66.90 

43.86 

06.71 

44.15 

66.52 

44.45 

80 

81 

67.93 

44.12 

67.74 

44.41 

67.54 

44.71 

67.35 

45.00 

81 

82 

08.77 

44.66 

68.58 

44.96 

08.38 

45.26 

68.18 

45.56 

82 

83 

69.01 

45.20 

69.41 

45.51 

09.21 

45.81 

69.01 

46.11 

83 

84 

70.45 

45  .  75 

70.25 

46  .  06 

70.05 

40.36 

09.84 

46  .  67 

84 

85 

71.29 

46.29 

71.08 

46.60 

70.88 

46.91 

70.07 

47.22 

85 

86 

72.13 

4S.84 

71.92 

47.15 

71.71 

47.47 

71.51 

47.78 

80 

87 

72.96 

47.38 

72.76 

47.70 

72.55 

48.02 

72.34 

48.33 

87 

88 

73.80 

47.93 

73.59 

48.25 

73.38  U8.57 

73.17 

48.89 

88 

89 

74  .  64 

48.47 

74.43 

48.80 

74.22 

49.12 

74.00 

49.45 

89 

90 

75.48 

49.02 

75.27 

49.35 

75.05 

49.07 

74.83 

50.00 

90 

91 

76.32 

49.56 

76.10 

49.89 

75.88 

50.23 

75  .  06 

50.56 

91 

92 

77.16 

50  .  1  1 

76.94 

50  .  44 

76.72 

50.78 

76.50 

51.11 

92 

93 

78.00 

50.05 

77.77 

50  .  99 

77.55 

51.33 

77.33 

51.67 

93 

94 

78.83 

51.20 

78.61 

51.54 

78.39 

51.88 

78.16 

52.22 

94 

95 

79.07 

51.74 

79.45 

52.09 

79.22 

52.43 

78.99 

52.78 

95 

96 

80.51 

52.29 

80.28 

52.64 

80.05 

52.99 

79.82 

53.33 

90 

97 

81.35 

52.83 

81.12 

53.18 

80.89 

53.54 

80.65 

53.  $9 

97 

98 

82.19 

53.37 

81.96 

53.73 

81.72 

54.09 

81.48 

54.45 

98 

99 

83.03 

53.92 

82.79 

54.28 

82.55 

54.04 

82.32 

55.00 

99 

100 

83.87 

54.46 

83.63 

54.83 

83.39 

55.19 

83.15 

55.56 

100 

0 

o 

D 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

rt 

.J8 

57  Deg. 

56|  Dcg. 

561  Deg. 

56$  Deg. 

rt 

.2 

a 

70 


TRAVERSE    TABLE. 


o 

34  Deg. 

344  Deg. 

34^  Deg. 

34|  Deg. 

D 

I 

£' 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1 

0.83 

0.56 

0.83 

0.56 

~~(JY82~ 

0.57 

0.  82 

0.57 

1 

2 

1.66 

1.12 

1.65 

1.13 

1.65 

1.13 

1.64 

1.14 

2 

'3 

2.49 

1.68 

2.48 

1.69 

2.47 

1.70 

2.46 

1.71 

3 

4 

3.32 

2.24 

3.31 

2.25 

3.30 

2.27 

3.29 

2.28 

4 

5 

4.15 

2.80 

4.13 

2.81 

4.12 

2.83 

4.11 

2.85 

5 

6 

4.97 

3.36 

4.96 

3.38 

4.94 

3.40 

4.93 

3.42 

6 

7 

5.80 

3.91 

5.79 

3.94 

5.77 

3.96 

5  .  75 

3.99 

7 

8 

6.63 

4,47 

6.61 

4.50 

6.59 

4.53 

6.57 

4.56 

8 

9 

7.46 

5.03 

7.44 

5.07 

7.42 

5.10 

7.39 

5.13 

9 

10 

8.29 

5.59 

8.27 

5  .  63 

8.24 

5.66 

8.22 

5.70 

10 

11 

9.12 

6.15 

9.09 

6.19 

9.07 

6.23 

9.04 

6.27 

11 

12 

9.95 

6.71 

9.92 

6.75 

9.89 

6.80 

9.86 

6.84 

12 

13 

10.78 

7.27 

10.75 

7.32 

10.71 

7.36 

10.68 

7.41 

13 

14 

11.61 

-7.83 

11.57 

7.88 

11.54 

7.93 

11.50 

7.98 

14 

15 

12.44 

8.39 

12.40 

8.44 

12.36 

8.50 

12.32 

8  .  55 

15 

16 

13.26 

8.95 

13.23 

9.00 

13.19 

9.06 

13.15 

9.12 

16 

17 

14.09 

9.51 

14.05 

9.57 

14.01 

9.63 

13.97 

9.69 

17 

18 

14.92 

10.07 

14.88 

10.13 

14.83 

10.20 

14,79 

10.26 

18 

19 

15.75 

10.62 

15.71 

10.69 

15.66 

10.76 

15.61 

10.83 

19 

20 

16.58 

11.18 

16.53 

11.26 

16.48 

11.33 

16.43 

11.40 

20 

21 

17.41 

11.74 

17.36 

11.82 

17.31 

11.89 

17.25 

11.97 

21 

22 

18.24 

12.30 

18.18 

12.38 

18.13 

12.46 

18.08 

12.54 

22 

23 

19.07 

12.86 

19.01 

12.94 

18.95 

13.03 

18.90 

13.11 

23 

24 

19.90 

13.42 

19.84 

13.51 

19.78 

13.59 

19.72 

13.68 

24 

25 

20  .  73 

13.98 

20.66 

14.07 

20.60 

14.16  i 

20.54 

14.25 

25 

26 

21.55 

14.54 

21.49 

14.63 

21.43 

14.73 

21.36 

14.82 

20 

27 

22.38 

15.10 

22.32 

15.20 

22.25 

15.29 

22.18 

15.39 

27 

28 

23.21 

15  66 

23.14 

15.76 

23.08 

15.86 

23.01 

15.96. 

28 

29 

24.04 

16.22 

23.97 

16.32 

23.90 

16.43 

23.83 

16.53 

29 

30 

24.87 

16.78 

24.80 

16.88 

24.72 

16.99 

24.65 

17.10 

30 

31 

25.70  17.33 

25.62 

17.45 

25  .  55 

17.56  1 

25.47 

17.67 

31 

32 

26.53  17.89 

26.45 

18.01 

26.37 

18.12 

26.29 

18.24 

32 

33 

27.36 

18.45 

27.28 

18.57 

27.20 

18.69 

27.11 

18.81 

33 

34 

28.19 

19.01 

28.10 

19.14 

28.02 

19.26 

27.94 

19.38 

34 

35 

29.02 

19.57 

28.93 

19.70 

28.84 

19.82 

28  .  76 

19.95 

35 

36 

29.85 

20.13 

29.76 

20.26 

29.67 

20.39 

29  .  58 

20  .  52 

36 

37 

30.67 

20.69 

30  .  58 

20.82 

30.49 

20.96 

30.40 

21.09 

37 

38 

31.50 

21.25 

31.41 

21.39 

31.32 

21.52 

31.22 

21.66 

38 

39 

32.33 

21.81 

32.24 

21.95 

32.14 

22.09 

32.04 

22.23 

39 

40 

33.16 

22  .  37 

33.06 

22.51 

32.97 

22  .  66 

32.87 

22.80 

40 

41 

33.99 

22.93 

33.89 

23.07 

33  .  79 

23.22 

33.69 

23.37 

41 

42 

34.82 

23.49 

34.72 

23.64 

34.61 

23.79 

34.51 

23  .  94 

42 

43 

35.65 

24.05 

35.54 

24.20 

35.44 

24.36 

35.33 

24.51 

43 

44 

36.48 

24.60 

36.37 

24.76 

36.26 

24.92 

36.15 

25.08 

41 

45 

37.31 

25.16 

37.20 

25.33 

37.09 

25.49 

36.97 

25.65 

45 

46 

38.14 

25.72 

38.02 

25.89 

37.91 

26.05 

37.80 

26.22 

46 

47 

38.96 

26.28 

38.85 

26.45 

38.73 

26.62 

38.62 

26.79 

47 

48 

39.79 

26.84 

39.68 

27.01 

39.56 

27.19 

39.44 

27.36 

48 

49 

40.62 

27.40 

40.50 

27.58 

40.38 

27.75 

40.26 

27  .  93 

49 

50 

41.45 

27.96 

41.33 

28.14 

41.21 

28.32 

41.08 

28.50 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

c 

E 

cd 

Q 

56  Deg. 

55|  Deg. 

55±  Deg. 

554  Deg.- 

Q 

TRAVERSE    TABLE, 


71 


o 
£' 

p 

34Deg. 

34}  Deg. 

34£  Deg. 

34|  Deg. 

| 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

s 
n 

CD 

~5l 

42.28 

28.52 

42.16 

28.70 

42.03 

28.89 

41.90 

29.07 

"tl 

52 

43.11 

29.08 

42.98 

29.27 

42.85 

29.45 

42,73 

29.64 

52 

53 

43.94 

29.64 

43.81 

29.83 

43.68 

30.02 

43.55 

30.21 

53 

54 

44.77 

30.20 

44.64 

30.39 

44.50 

30.59 

44.37 

30.78 

54 

55 

45,  60 

30.76 

45.46 

30.95 

45.33 

31.15 

45.19 

31.35 

55 

56 

46.43 

31.31 

46.29 

31.52 

46.15 

31.72 

46.01 

31.92 

56 

57 

47.26 

31.87 

47.12" 

32.08 

46.98 

32.29 

46.83 

32.49 

57 

58 

48.08 

32.43 

47.94 

32.64 

47.80 

32.85 

47.66 

33.06 

58 

59 

48.91 

32.99 

48.77 

33.21 

48  .  62 

33  .  42 

48.48 

33.63 

59 

60 

49,74 

33.55 

49.60 

33.77 

49.45 

33.98 

49.30 

34.20 

60 

61 

50.57 

34.11 

50.42 

34.33 

50.27 

34.55 

50.12 

34.77 

61 

62 

51.40 

34.67 

51.25 

34.89 

51.  10 

35.12 

50.94 

35.34 

62 

63 

52.23 

35.23 

52.08 

35.46 

51.92 

35.68 

51.76 

35.91 

63 

64 

53.06 

35.79 

52.90 

36.02 

52  .  74 

36.25 

52.59 

36.48 

64 

65 

53.89 

36  35 

53.73 

36.58 

53.57 

36.82 

53.41 

37.05 

65 

66 

54.72 

36.91 

54.55 

37.15 

54.39 

37.38 

54.23 

37.62 

66 

67 

55.55 

37.46 

55.38 

37.71 

55.22 

37.95 

55.05 

38.19 

67 

68 

56.37 

38.03 

56.21 

38.27 

56.04 

38  .  52 

55.87 

38  .  76 

68 

69 

57.20 

38.58 

57.03 

38.83 

56.86 

39.08 

56.69 

39.33 

69 

70 

58,03 

39.14 

57.86 

39.40 

57.69 

39.65 

57.52 

39.90 

70 

71 

58.86 

39.70 

58.69 

39  .  96 

58.51 

40.21 

58.34 

40.47 

71 

72 

59.69 

40.26 

59.51 

40  .  52 

59.34 

40.78 

59.16 

41.04 

72 

73 

60.52 

40.82 

60.34 

41.08 

60.16 

41.35 

59.98 

41.61 

73 

74 

61.35 

41.38 

61.17 

41.65 

60.99 

41.91 

60.80 

42.18 

74 

75 

62.18 

41.94 

61.99 

42.21 

61.81 

42.48 

61.62 

42.75 

75 

76 

63.01 

42.50 

62.82 

42.77 

62.63 

43.05 

62.45 

43.32 

76 

77 

63.84 

43.06 

63.65 

43.34 

63.46 

43.61 

63.27 

43.89 

77 

78 

64.66 

43.62 

64.47 

43.90 

64.28 

44.18 

64.09 

44.46 

78 

79 

65.49 

44.18 

65.30 

44.46 

65.11 

44.75 

64.91 

45.03 

79 

80 

66.32 

44.74 

66,13 

45.02 

65.93 

45.31 

65.73 

45  .  60 

80 

81 

67.15 

45.29 

66.95 

45.59" 

66  .  75 

45.88 

66.55 

46.17 

81 

82 

67.98 

45.85 

67.78 

•46.15 

67.58 

46.45 

67.37 

46.74 

82 

83 

68.81 

46.41 

68.61 

46.71 

68.40 

47.01 

68.20 

47.31 

83 

84 

69,64 

46.97 

69.43 

47.28 

69.23 

47.58 

69.02 

47.88 

84 

€5 

70.47 

47.53 

70.26 

47.84 

70.05 

48.14 

69.84 

48.45 

85 

86 

71.30 

48.09 

71.09 

48.40 

70.87 

48.71 

70.66 

49.02 

86 

87 

72.13 

48.65 

71.91 

48.96 

71.70 

49.28 

71.48 

49.59 

87 

88 

72.96 

49.21 

72.74 

49.53 

72.52 

49.84 

72.30 

50.16 

88 

89 

73  .  78 

49.77 

73.57 

50.09 

73.35 

50.41 

73.13 

50.73 

89 

90 

74.61 

50.33 

74.39 

50  .  65 

74.17 

50,98 

73  .  95 

51.30 

90 

91 

75.44 

50,89 

75.22 

51.22 

75  .  00 

51.54 

74.77 

51.87 

91 

92 

76.27 

51.45 

76.05 

51.78 

75.82 

52.11 

75.59 

52.44 

92 

93 

77.10 

52.00 

76.87 

52.34 

76.64 

52.68 

76.41 

53.01 

93 

94 

77.93 

52.56 

77.70 

52.90 

77.47 

53.24 

77.23 

53.58 

94 

95 

78.76 

53.12 

78.53 

53,47 

78.29 

53.81 

78.06 

54.151    95 

96 

79.59 

53.68 

79.35 

54.03 

79.12 

54.37 

78.88 

54.72      96 

97 

80.42 

54.24 

80.18 

54.59 

79.94 

54.94 

79.70 

55.29 

97 

98 

81.25 

54.80 

81.01 

55.15 

80.76 

55.51 

80.52 

55.86 

98 

99 

82.07 

55.36 

81.83 

55.72 

81.59 

56.07 

81.34 

56.43 

99 

100 

82.90 

55.92 

82.66 

56.28 

82.41 

56.64 

82.16 

57.00 

100 

5 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

1 

1 

Q 

56  Deg. 

55J  Deg. 

55£  Deg. 

55i  Deg. 

.2 
Q 

72 


TRAVERSE   TABLE. 


d 

35  Deg. 

354  Deg. 

35i  Deg. 

35|  Deg. 

O 

1 

8 

.stance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

0.82 

0.57 

0.82 

0.58 

0.81 

0.58 

0.81 

~0^58~ 

1 

2 

1.64 

1.15 

1.63 

1.15 

1.63 

1.16 

1.62 

1.17 

2 

3 

2.46 

1.72 

2.45 

1.73 

2.44 

1.74 

2.43 

1.75 

3 

4 

3.28 

2.29 

3.27 

2.31 

3.26 

2.32 

3.25 

2.34 

4 

5 

4.10 

2.87 

4.08 

2.89 

4.07 

2.90 

4.06 

2.92 

5 

6 

4.91 

3.44 

4.90 

3.46 

4.88 

3.48 

4.87 

3.51 

6 

7 

5.73 

4.01 

5.72 

4.04 

5.70 

4.06 

5.68 

4.09 

7 

8 

6.55 

4.59 

6.53 

4.62 

6.51 

4.65 

6.49 

4.67 

8 

9 

7.37 

5.16 

7.35 

5.19 

7.33 

5.23 

7.30 

5.26 

9 

10 

8.19 

5.74 

8.17 

5.77 

8.14 

5.81 

8.12 

5.84 

10 

"  11 

9.01 

0.31 

8.98 

6.35 

8.96 

6.39 

8.93 

6.43 

if 

12 

9.83 

6.88 

9.80 

6.93 

9.77 

6.97 

9.74 

7.01 

12 

13 

10.65 

7.46 

10.62 

7.50 

10.58 

7.55 

10.55 

7.60 

13 

14 

11.47 

8.03 

11.43 

8.08 

11.40 

8.13 

11.36 

8.18 

14 

15 

12.29 

8.60 

12.25 

8.66 

12.21 

8.71 

12.17 

8.76 

15 

16 

13.11 

9.18 

13.07 

9.23 

13.03 

9.29 

12.99 

9.35 

16 

17 

13.93 

9.75 

13.88 

9.81 

13.84 

9.87 

13.80 

9.93 

17 

18 

14.74 

10.32 

14.70 

10.39 

14.65 

10.45 

14.61 

10.52 

18 

19 

15.56 

10.90 

15.52 

10.97 

15.47 

11.03 

15.42 

11.10 

19 

20 

16.38 

11.47 

16.33 

11.54 

16.28 

11.61 

16.23 

11.68 

20 

21 

17.20 

12.05 

17.15 

12.12 

17.10 

12.19 

17.04 

12.27 

21 

22 

18.02 

12.62 

17.97 

12.70 

17.91 

12.78 

17.85 

12.85 

22 

23 

18.84 

13.19 

18.78 

13.27 

18.72 

13.36 

18.67 

13.44 

23 

24 

19.66 

13.77 

19.60 

13.85 

19.54 

13.94 

19.48 

14.02 

24 

25 

20.48 

14.34 

20.42 

14.43 

20.35 

14.52 

20.29 

14.61 

25 

26 

21.30 

14.91 

21.23 

15.01 

21.17 

15.10 

21.10 

15.19 

26 

27 

22.12 

15.49 

22.05 

15.58 

21.98 

15.68 

21.91 

15.77 

27 

28 

22.94 

16.06 

22.87 

16.16 

22.80 

16.26 

22.72 

16.36 

28 

29 

23  .  76 

16.63 

23.68 

16.74 

23.61 

16.84 

23.54 

16.94 

29 

30 

24  .  57 

17.21 

24.50 

17.31 

24.42 

17.42 

24.35 

17.53 

30 

31 

25.39 

17.78 

25.32 

17.89 

25.24 

18.00 

25.16 

18.11 

31 

32 

26.21 

18.35 

26.13 

18.47 

26.05 

18.58 

25.97 

18.70 

32 

33 

27.03 

18.93 

26.95 

19.05 

26.87 

19.16 

26.78 

19.28 

33 

34 

27.85 

19.50 

27.77 

19.62 

27.68 

19.74 

27.59 

19.86 

34 

35 

28  .  67 

20.08 

28.58 

20.20 

28.49 

20.32 

28.41 

20.45 

35 

36 

29.49 

20.65 

29.40 

20  .  78 

29.31 

20.91 

29.22 

21.03 

36 

37 

30.31 

21.22 

30.22 

21.35 

30.12 

21.49 

30.03 

21.62 

37 

38 

31.13 

21.80 

31.03 

21.93 

30.94 

22.07 

30.84 

22.20 

38 

39 

31.95 

22.37 

31.85 

22.51 

31.75 

22.65 

31.65 

22.79 

39 

40 

32.77 

22.94 

32.67 

23.09 

32.56 

23.23 

32.46 

23.37 

40 

41 

33.59 

23.52 

33.48 

23.66 

33.  3S 

23.81 

33.27 

23.95 

41 

42 

34.40 

24.09 

34.30 

24.24 

34.19 

24.39 

34.09 

24.54 

42 

43 

35.22 

24.66 

35.12 

24.82 

35.01 

24.97 

34.90 

25.12 

43 

44 

36.04 

25  .  24 

35.93 

25.39 

35.82 

25.55 

35.71 

25.71 

44 

45 

36.86 

25.81 

36.75 

25.97 

36.64 

26.13 

36.52 

26.29 

45 

46 

37.68 

26.38 

37.57 

26.55 

37.45 

26.71 

37.33 

26.88 

46 

47 

38.50 

26.96 

38.38 

27.13 

38.26 

27.29 

38.14 

27.46 

47 

48 

39.32 

27.53 

39.20 

27.70 

39.08 

27.87 

38.96 

28.04 

48 

49 

40.14 

28.11 

40.02 

28.28 

39.89 

28.45 

39.77 

28.63 

49 

50 

40.96 

28.68 

40.83 

28  .  86 

40.71 

29.04 

40.58 

29.21 

50 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

a 

1 

Q 

55  Deg. 

54|  Deg. 

54£  Deg. 

544  Deg. 

.a 
a 

TRAVERSE   TABLE. 


73 


f 

35  Deg. 

35}  Deg. 

35£  Deg. 

35|  Deg. 

s 

o 
<s 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 
p 

51 

41.78 

29.25 

41.65 

29.43 

41.52 

29.62 

41.39 

29.80 

51 

52 

42.60 

29.83 

42.47 

30.01 

42.33 

30.20 

42.20 

30.38 

52 

53 

43.42 

30.40 

43.28 

30.59 

43.15 

30.78 

43.01 

30.97 

53 

54 

44.23 

30.97 

44.10 

31.17 

43.96 

31.36 

43.82 

31.55 

54 

55 

45.05 

31.55 

44.92 

31.74 

44.78 

31.94 

44.64 

32.13 

55 

56 

45.87 

32.12 

45.73 

32.32 

45.59 

32.52 

45.45 

32.72 

56 

57 

46.69 

32.69 

46.55 

32.90 

46.40 

33.10 

46.26 

33.30 

57 

58 

47.51 

33.27 

47.37 

33.47 

47.22 

33.68 

47.07 

33.89 

58 

59 

43.33 

33.84 

48.18 

34.05 

48.03 

34.26 

47.88 

34.47 

59 

60 

49.15 

34.41 

49.00 

34.63 

48.85 

34.84 

48.69 

35.05 

60 

61 

49.97 

34.99 

49.82 

35.21 

49.66 

35.42 

49.51 

35.64" 

61 

62 

50.79 

35.56 

50.63 

35.78 

50.48 

36.00 

50.32 

36.22 

62 

63 

51.61 

36.14 

51.45 

36.36 

51.29 

36.58 

51.13 

36.81 

63 

64 

52.43 

36.71 

52.27 

36.94 

52.10 

37.  16 

51.94 

37.39 

64 

65 

53.24 

37.28 

53.08 

37.51 

52.92 

37.75 

52.75 

37.98 

65 

66 

54.06 

37  ..86 

53.90 

38.09 

53.73 

38.33 

53.56 

38.56 

66 

67 

54.88 

38.43 

54.71 

38.67 

54.55 

38.91 

54.38 

39  .  14 

67 

68 

55  .  70 

39.00 

55.53 

39.25 

55.36 

39.49 

55.19 

39.73 

68 

69 

56  .  52 

39.58 

56.35 

39.82 

56.17 

40.07 

56.00 

40.31 

69 

70 

57.34 

40.15 

57.  1C 

40  40 

56.99 

40.65 

56.81 

40.90 

70 

71 

58.16 

40  .  72 

57.98 

40.98 

57.80 

41.23 

57.62 

41.48 

71 

72 

58.98 

41.30 

58.80 

41.55 

58.62 

41.81 

58.43 

42.07 

72 

73 

59.80 

41.87 

59.61 

42.13 

59.43 

42.39 

59.24 

42.65 

73 

74 

60.62 

42.44 

60.43 

42.71 

60.24 

42.97 

60.06 

43.23 

74 

75 

61.44 

43.02 

61.25 

43.29 

61.06 

43.55 

60.87 

43.82 

75 

76 

ea.se 

43  .  59 

R2.06 

43.86 

61.87 

44.13 

61.68 

44.40 

76 

77 

63.07 

44.17 

62.88 

44.44 

62.69 

44.71 

62.49 

44.99 

77 

78 

63.89 

44.74 

63.70 

45.02 

63.50 

45  .  29 

63.30 

45.57 

78 

79 

64.71 

45.31 

64.51 

45.59 

64.32 

45.88 

64.11 

46.16 

79 

80 

65.53 

45.89 

65.33 

46.17 

65.13 

46.46 

64.93 

46.74 

80 

81 

66.35 

46.46 

66.15 

46.75 

65.94 

47.04 

65.74 

47.32 

81 

82 

67.17 

47.03 

66.96 

47.33 

66.76 

47.62 

66.55 

47.91 

82 

83 

67.99 

47.61 

67.  78 

47.90 

67.57 

48.20 

67.36 

48.49 

83 

84 

68.81 

48.18 

68.60 

48.48 

68.39 

48.78 

68.17 

49.08 

84 

85 

69.63 

48.75 

69.41 

49.06 

69.20 

49.36 

68.98 

49.66 

85 

86 

70.45 

49.33 

70.23 

49.63 

70.01 

49.94 

69.80 

50.25 

86 

87 

71.27 

49.90 

71.05 

50.21 

70.83 

50.52 

70.61 

50.83 

87 

88 

73.09 

50.47 

71.86 

50.79 

71.64 

51.10 

71.42 

51.41 

88 

89 

72.90 

51.05 

72.68 

51.37 

72.46 

51.68 

72.23 

52.00 

89 

90 

73.72 

51.62 

73.50 

51.94 

52.26 

73  .  04 

52.58 

90 

91 

74.54 

52.20 

74  .-31 

52.52 

74708~' 

52.84 

73.85 

53.17 

91 

92 

75.36 

52  .  77 

75.13 

53.10 

74.90 

53.42 

74.66 

53.75 

92 

93 

76.18 

53.34 

75.95 

53.67 

75.71 

54.01 

75.48 

54.34 

93 

94 

77.00 

53.92 

76.76 

54.25 

76.53 

54.59 

76.29 

54.92 

94 

95 

77.82 

54.49 

77.58 

54.83 

77.34 

55.17 

77.10 

55.50 

95 

96 

78.64 

55.06 

78.40 

55.41 

78.16 

55.75 

77.91 

56.09 

96 

97 

79.46 

55.64 

79.21 

55.98 

78.97 

56.33 

78.72 

56.67 

97 

98 

80.28 

56.21 

80.03 

56.56 

79.78 

56.91 

79.53 

57.26 

98 

99 

81.10 

56.78 

80.85 

57.14 

80.60 

57.49 

80.35 

57.84 

99 

100 

81.92 

57.36 

81.66 

57.71 

81.41 

58.07 

81.16 

58.42 

o 

e 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

1 

5 
« 

55  Deg. 

54|  Deg. 

544  Deg. 

54}  Deg. 

Q 

74 


TRAVERSE 


o 

36  Deg. 

36iDeg. 

36f  Deg. 

36|  Deg. 

b 

1" 

55" 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

1 

0.81 

0.59 

0.81 

0.59 

0.80 

0.59 

0.80 

0.60 

] 

2 

1.62 

1.18 

1.61 

1.18 

1.61 

1.19 

1.60 

1.20 

2 

3 

2.43 

1.76 

2.42 

1.77 

2.41 

1.78 

2.40 

1.79 

» 

4 

3.24 

2.35 

3.23 

2.37 

3.22 

2.38 

3.20 

2.39 

4 

5 

4.05 

2.94 

4.03 

2.96 

4.02 

2.97 

4.01 

2,99 

P 

6 

4.85 

3.53 

4.84 

3.55 

4.82 

3.57 

4,81 

3.59 

e 

7 

5.66 

4.11 

5.65 

4.U 

5.63 

4.16 

5.61 

4.19 

"3 

8 

6.47 

4.70 

6.45 

4.73 

6.43 

4.76 

6,41 

4.79 

8 

9 

7.28 

5,29 

7.26 

5.32 

7.23 

5.35 

7,21 

5.3S 

c 

10 

8.09 

5.88 

8.06 

5.91 

8.04 

5.95 

8.01 

5,98 

10 

11 

8.90 

6.47 

8.87 

6.50 

8.84 

6.54 

8.81 

6.58 

11 

12 

9.71 

7.05 

9.68 

7.10 

9.65 

7.14 

9.61 

7.18 

12 

13 

10.52 

7.64 

10.48 

7.69 

10.45 

7,73 

10.42 

7.78 

13 

14 

11.33 

8.23 

11.29 

8.28 

11.25 

8.33 

11.22 

8.38 

14 

15 

12.14 

8.82 

12.10 

8.87 

12.06 

8.92 

12.02 

8.97 

15 

16 

12.94 

9.40 

12.90 

9.46 

12.86 

9.52 

12,82 

9.57 

16 

17 

13.75 

9.99 

13.71 

10.05 

13.67 

10.11 

13.62 

10.17 

17 

18 

14.56 

10.58 

14.52 

10.64 

14.47 

10,71 

14.42 

10.77 

18 

19 

15.37 

11.17 

15.32 

11.23 

15.27 

11.30 

15.22 

11.37 

19 

20 

16.18 

11.76 

16.13 

11.83 

16.08 

11,90 

16.03 

11.97 

20 

21 

16.99 

12.34 

16.94 

12.42 

16.88 

12.49 

16.83 

12.56 

21 

22 

17.80 

12.93 

17,74 

13.01 

17.68 

13.09 

17.63 

13.16 

22 

23 

18.61 

13.52 

18.55 

13.60 

18,49 

13.68 

18.43 

13.76 

23 

24 

19.42 

14.11 

19,35 

14.  19' 

19v29 

14.28 

19.23 

14.36 

25 

20.23 

14.69 

20.16 

14.78 

20.10 

14.87 

20.03 

14.96 

25 

26 

21.03 

15.28 

20.97 

15.37 

9ft-.  DO 

15.47 

SO.  83 

1  5  .  50 

26 

27 

21.84 

15.87 

21.77 

15.97 

21.70 

16.06 

21.63 

16.15 

27 

28 

22.65 

16.46 

22.58 

16.56 

22.51 

16.65 

22.44 

16.75 

28 

29 

23.46 

17.05 

23.39 

17.15 

23.31 

17.25 

23.24 

17.35 

29 

30 

24.27 

17.63 

24.19 

17.74 

24.12 

17.84 

24.04 

17.95 

30 

31 

25.08 

18.22 

25.00 

18.33 

24.92 

18.44 

24.84 

18.55 

31 

32 

25.89 

18.81 

25.81 

18.92 

25.72 

19.03 

25.64 

19.15 

32 

33 

26.70 

19.40 

26.61 

19.51 

26.53 

19.63 

26.44 

19.74 

33 

34 

27.51 

19.98 

27.42 

20.10 

27.33 

20.22 

27.24 

20.34 

34 

35 

28.32 

20.57 

28.23 

20.70 

28.13 

20.82 

28.04 

20.94 

35 

36 

29.12 

21.16 

29.03 

21.29 

28.94 

21.41 

28.85 

21.54 

36 

37 

29.93 

21.75 

29.84 

21.88 

29.74 

22.01 

29.65 

22.14 

37 

38 

30.74 

22.34 

30.64 

22.47 

30.55 

22.60 

30.45 

22.74 

38 

39 

31.55 

22.92 

31.45 

23.06 

31.35 

23.20 

31.25 

23.33 

39 

40 

32.36 

23.51 

32.26 

23.65 

32.15 

23.79 

32.05 

23.93 

40 

41 

33.17 

24.10 

33.06 

24.24 

32.96 

24.39 

32.85 

24.53 

41 

42 

33.98 

24.69 

33.87 

24.83 

33.76 

24.98 

33:.  65 

25.13 

42 

43 

34.79 

25.27 

34.68 

25.43 

34.57 

25.58 

34.45 

25.73 

43 

44 

35.60 

25.86 

35.48 

26.02 

35.37 

26.17 

35.26 

26.33 

44 

45 

36.41 

26.45 

36.29 

26.61 

36.17 

26.77 

36.06 

26.92 

45 

46 

37.21 

27.04 

37.10 

27.20 

36.98 

27.36 

36.86 

27.52 

46 

47 

38.02 

27.63 

37.90 

27.79 

37.78 

27.96 

37.66 

28.12 

47 

48 

38.83 

28.21 

38.71 

28.38 

38.59 

28.55 

38.46 

28.72 

48 

49 

39.64 

28.80 

39.52 

28.97 

39.39 

29.15 

39.26 

2,9,32 

49 

50 

40.45 

29.39 

40.32 

29.57 

40.19 

29.74 

40.06 

29.92 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

1 

54  Deg. 

53|  Deg. 

53J  Deg. 

53i  Deg. 

od 

3 

TRAVERSE    TABLE. 


E 

36  Deg. 

364  Deg. 

36  £  Deg. 

36|  Deg. 

O 

P 

Lat. 

Dep 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

51 

41.26 

29.9 

41.13 

30.16 

41.00 

30.34 

40.86 

30.51 

51 

52 

42.07 

30.5 

41.94 

30.75 

41.80 

30.93 

41.67 

31.11 

52 

53 

42.88 

31.15 

42.74 

31.34 

42.60 

31.53 

42.47 

31.71 

53 

54 

43.69 

31.74 

43.55 

31.93 

43.41 

32.12 

43.27 

32.31 

54 

55 

44.50 

32.33 

44.35 

32.52 

44.21 

32.72 

44.07 

32.91 

55 

56 

45.30 

32.92 

45.  If 

33.11 

45.02 

33.31 

44.87 

33.51 

56 

57 

46.11 

33.50 

45.97 

33.70 

45.82 

33.90 

45.67 

34.10 

57 

58 

46.92 

34.09 

46.77 

34.30 

46.62 

34.50 

46.47 

34.70 

58 

59 

47.73 

34.68 

47.58 

34.89 

47.43 

35  09 

47.27 

35.30 

59 

60 

48.54 

35.27 

48.39 

35.48 

48.23 

35.69 

48.08 

35.90 

60 

61 

49.35 

35.85 

49.19 

36.07 

49.04 

36.28 

48.88 

36.50 

61 

62 

50.16 

36.44 

50.00 

36,66 

49.84 

36.88 

49.68 

37.10 

62 

63 

50.97 

37.03 

50.81 

37.25 

50.64 

37.47 

50.48 

37.69 

-  63 

64 

51.78 

37.62 

51.61 

37.84 

51.45 

38.07 

51.28 

38.29 

64 

65 

52.59 

38,21 

52.42 

38.44 

52.25 

38.66 

52.08 

38.89 

65 

66 

53.40 

38.79 

53.23 

39.03 

53.05 

39.26 

52.88 

39.49 

66 

67 

54.20 

39.38 

54.03 

39  .  62 

53.86 

39.85 

53.68 

40.09 

67 

68 

55.01 

39.97 

54.84 

40,21 

54.66 

40.45 

54.49 

40.69 

68 

69 

55.82 

40.56 

55.64 

40.80 

55.47 

41.04 

55.29 

41.28 

69 

70 

56.63 

41.14 

56.45 

41.39 

56.27 

41.64 

56.09 

41.88 

70 

71 

57.44 

41.73 

57.26 

41.98 

57  ."07 

42.23 

56.89 

42.48 

71 

72 

58.25 

42.32 

58.06 

42.57 

57.88 

42.83 

57.69 

43.08 

72 

73 

59.06 

42.91 

58.87 

43.17 

58.68 

43.42 

58.49 

43.68 

73 

74 

59.87 

43.50 

59.68 

43.76 

59.49 

44.02 

59.29 

44.28 

74 

75 

60.68 

44.08 

60.48 

44.35 

60.29 

44.61 

60.09 

44.87 

75 

76 

61.49 

44.67 

61.29 

44.94 

61.09 

45.21 

60.90 

45.47 

76 

77 

62.29 

45.26 

62.10 

45.53 

61.90 

45.80 

61.70 

46.07 

77 

78 

63.10 

45.85 

62.90 

46.12 

62  .  70 

46.40 

62.50 

46.67 

78 

79 

63.91 

46.43 

63.71 

46.71 

63.50 

46.99 

63.30 

47.27 

79 

80 

64.72 

47.02 

64.52 

47.30 

64.31 

47.59 

64.10 

47.87 

80 

81 

65.53 

47.61 

65.32 

47.90 

65.11 

48.18 

64.90 

48.46 

81 

82 

66.34 

48.20 

66.13 

48.49 

65.92 

48.78 

65.70. 

49.06 

82 

83 

67.15 

48.79 

66.93 

49.08 

66.72 

49.37 

66.50 

49.66 

83 

84 

67.96 

49.37 

67.74 

49.67 

67.52 

49.97 

67.31 

50.26 

84 

85 

68.77 

49.96 

68.55 

50.26 

68.33 

50.56 

68.11 

50.86 

85 

86 

69.58 

50.55 

69.35 

50.85 

69.13 

51.15 

68.91 

51.46 

86 

87 

70,38 

51.14 

70.16 

51.44 

69.94 

51.75 

69.71 

52.05 

87 

88 

71,19 

1.73 

70.97 

52.04 

70.74 

52.34 

70.51 

52  .  65 

88 

89 

72,00 

2.31 

71.77 

52.63 

71.54 

52.94 

71.31 

53.25 

89 

90 

72.81 

2.90 

72.58 

53.22 

72.35 

53.53 

72.11 

53.85 

90 

91 

73.62 

53.49 

73.39 

53.81 

73.15 

54.13 

72.91 

54.45 

91 

92 

74.43 

54.08 

74.19 

54.40 

73.95 

54.72 

73.72 

55.05 

92 

93 

75.24 

54.66 

75.00 

54.99 

74.76 

55.32 

74.52 

55.64 

93 

94 

76,05 

55.25 

75.81 

55.58 

75.56 

55.91 

75.32 

56.24 

94 

95 

76.86 

55.84 

76.61 

56.17 

76.37 

56.51 

76.12 

56.84 

95 

96 

77.67 

56.43 

7.42 

56.77 

77.17 

57.10 

76.92 

57.44 

96 

97 

78.47 

57.02 

8.23 

57.36 

77.97 

57.70 

77.72 

58.04 

97 

98 

79.28 

57.60 

79.03 

57.95 

'8.78 

58.29 

78.52 

58.64 

98 

99 

80.09 

58.19 

9.84 

58.54 

79.58 

58.89 

79.32 

59.23 

99 

100 

80.90 

58.78 

0.64 

59.13 

80.39 

59.48 

80.13 

59.83 

00 

B 
U 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

I 

54  Deg. 

53|  Deg. 

53i  Deg. 

534  Deg. 

Q 

12* 


76 


TRAVERSE   TABLE. 


d 

87  Deg. 

374  Deg. 

37£  Deg. 

37|  Deg. 

c 

S- 

5.' 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

~T 

0  80~ 

0.60 

0.80 

0.61 

0.79 

0.61 

0.79 

0.61 

i 

2 

i!eo 

1.20 

1.59 

1.21 

1.59 

1.22 

1.58 

1  .22 

2 

3 

2.40 

1.81 

2.39 

1.82 

2.38 

1.83 

2.37 

1.84 

3 

4 

3.19 

2.41 

3.18 

2.42 

3.17 

2.13 

3.16 

2.45 

4 

5 

3.99 

3.01 

3.98 

3.03 

3.97 

3.04 

3.95 

3.06 

5 

6 

4.79 

3.61 

4.78 

3.63 

4.76 

3.65 

4.74 

3.67 

6 

7 

5.59 

4.21 

5.57 

4.24 

5.55 

4.26 

5.53 

4.29 

7 

8 

6.39 

4.81 

6.37 

4.84 

6.35 

4.87 

6.33 

4.90 

8 

9 

7.19 

5.42 

7.16 

5.45 

7.14 

5.48 

7.12 

5.51 

9 

10 

7.99 

6.02 

7.96 

6.05 

7.93 

6.09 

7.91 

6.12 

10 

11 

8.78 

6.62 

8.76 

6.66 

8.73 

6.70 

8.70 

6.73 

11 

12 

9.58 

7.22 

9.55 

7.26 

9.52 

7.31 

9.49 

7.35 

12 

13 

10.38 

7.82 

10.35 

7.87 

10.31 

7.91 

10.28 

7.96 

13 

14 

11.18 

8.43 

11.14 

8.47 

11.11 

8.52 

11.07 

8.57 

14 

15 

11.98 

9.03 

11.94 

9.08 

11.90 

9.13 

11.86 

9.18 

15 

16 

12.78 

9.63 

12.74 

9.68 

12.69 

9.74 

12.65 

9.80 

16 

17 

13.58 

10.23 

13.53 

10.29 

13.49 

10.35 

13.44 

10.41 

17 

18 

14.38 

10.83 

14.33 

10.90 

14.28 

10.96 

14.23 

11.02 

18 

19 

15.17 

11.43 

15.12 

11.50 

15.07 

11.57 

15.02 

11.63 

19 

20 

15.97 

12.04 

15.92 

12.11 

15.87 

12.18 

15.81 

12.24 

20 

21 

16.77 

12.64 

16.72 

12.71 

16.66 

12.78 

16.60|  12.80 

21 

22 

17.57 

13.24 

17.51 

13.32 

17.45 

13.39 

17.40 

13.47 

22 

23 

18.37 

13.84 

18.31 

13.92 

18.25 

14.00 

18.19 

14.08 

23 

24 

19.17 

14.44 

19.10 

14.53 

19.04 

14.61 

18.98 

14.69 

24 

25 

19.97 

15.05 

19.90 

15.13 

19.83 

15.22 

19.77 

15.31 

25 

26 

20.76 

15.65 

20.70 

15.74 

20.63 

15.83 

20.56 

15.92 

26 

27 

21.56 

16.25 

21.49 

16.34 

21.42 

16.44 

21.35 

16.53 

27 

28 

22.38 

16.85 

22.29 

16.95 

22.21 

17.05 

22.14 

17.14 

28 

29 

23.16 

17.45 

23.08 

17.55 

23'.  01 

17.65 

22,93 

17.75 

29 

30 

23.96 

18.05 

23.88 

18.16 

23.80 

18.26 

23.72 

18.37 

30 

31 

24.76 

18.66 

24.68 

18.76 

24.59 

18.87 

24.51 

18.98  1   31 

32 

25.56 

19.26 

25.47 

19.37 

25.39 

19.48 

25.30 

19.59  1   3-2 

33 

26.35 

19.80 

26.27 

19.97 

26.18 

20.09 

26.09 

20.20 

33 

34 

27.15 

20.46 

27.06 

20.58 

26.97 

20.70 

26.83 

20.82 

34 

35    27.95 

21.06 

27.86 

21.19 

27.77 

21.31 

27.67 

21.43 

35 

36 

28.75 

21.67 

28.66 

21.79 

23.56 

21.92 

28.46 

22.04 

35 

37 

29.55 

22.27 

29.45 

22.40 

29.35 

22.52 

29.26 

22.65 

37 

38 

30.35 

22.87 

30.25 

23.00 

30.15 

23.13 

30.05 

23.26 

33 

39 

31.15 

23.47 

31.04 

23.61 

30.94 

23.74 

30.84 

23.88 

39 

40 

31.95 

24.07 

31.84 

24.21 

31.73 

24.35 

31.63 

24.49 

40 

41 

32.74 

24.67 

32.64 

24.82 

32.53 

24.96 

32.42~ 

25.10 

41 

42 

33.54 

25.28 

33.43 

25.42 

33.32 

25.57 

33.21 

25.71 

42 

43 

34.34 

25.88 

34.23 

26.03 

34.11 

26.18 

34.00 

29.33 

43 

44 

35.14 

26.48 

35.02 

26.63 

34.91 

26.79 

34.79 

26.94 

44 

45 

35.94 

27.08 

35.82 

27.24 

35.70 

27.39 

35.58 

27.55 

45 

46 

36.74 

27.68 

36.62 

27.84 

36.49 

28.00 

36.37 

28.16 

46 

47 

37.54 

28.29 

37.41 

28.45 

37.29 

28.61 

37.16 

28.77 

47 

48 

38.33 

28.89 

38.21 

29.05 

38.08 

29.22 

37.95 

29.39 

43 

49 

39.13 

29.49 

39.00 

29.66 

38.87 

29.83 

38.74 

30.00 

49 

50 

39.93 

30.09 

39.80 

30.26 

39.67 

30.44 

39  .  53 

30.61 

50 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

CJ 

o 

-2 

1 

'& 

53  Deg. 

52|  Deg. 

52i  Deg. 

52J  Deg. 

Q 

TRAVERSE    TABLE. 


77 


d 

37  Deg. 

37*  Deg. 

37J  Deg. 

37|  Deg. 

0 

1' 

2. 

3 
o 
» 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

51 

40.73 

30.69 

40.60 

30.87 

40.46 

31.05 

40.33 

31.22 

51 

52 

41.53 

31.29 

41.39 

31.48 

41.25 

31.66 

41.12 

31.84 

52 

53 

42.33 

31.90 

42.19 

32.08 

42.05 

32.26 

41.91 

32.45 

53 

54 

43.13 

S>2.50 

42.98 

32.69 

42.84 

32.87 

42.70 

33.06 

54 

55 

43.92 

33.10 

43.78 

33.29 

43.63 

33.48 

43.49 

33.67 

55 

56 

44.72 

33.70 

44.58 

33.90 

44.43 

34.09 

44.28 

34.28 

56 

57 

45.52 

34.30 

45.37 

34.50 

45.22 

34.70 

45.07 

34.90 

57 

58 

46.32 

34.91 

46.17 

35.11 

46.01 

35.31 

45.86 

35.51 

58 

59 

47.12 

35.51 

46.96 

35.71 

46.81 

35.92 

46  .  65 

36.12 

59 

60 

47.92 

36.11 

47.76 

36.32 

47.60 

36.53 

47.44 

36.73 

60 

61 

48  .  72 

36.71 

48.56 

36.92 

48.39 

37.13 

48.23 

37.35 

61 

62 

49.52 

37.31 

49.35 

37.53 

49.19 

37.74 

49.02 

37.96 

62 

63 

50.31 

37.91 

50.15 

38.13 

49.98 

38.35 

49.81 

38.57 

63 

64 

51.11 

38.52 

50.94 

38.74 

50.77 

38.96 

50.60 

39.18 

64 

65 

51.91 

39.12 

51.74 

39.34 

51.57 

39.57 

51.39 

39.79 

65 

66 

52.71 

39.72 

52.54 

39.95 

52.36 

40.18 

52.19 

40.41 

66 

67 

53.51 

40.32 

53.33 

40.55 

53.15 

40.79 

52.98 

41.02 

67 

68 

54.31 

40.92 

54.13 

41.16 

53.95 

41.40 

53.77 

41.63 

68 

69 

55.11' 

41.53 

54  .  92 

41.77 

54.74 

42.00 

54.56 

42.24 

69 

70 

55.90 

42.13 

55.72 

42.37 

55.53 

42.61 

55.35 

42.86 

70 

~7l 

56.70 

42.73 

56.52 

42.98 

56.33 

43.22 

56.14 

43.47 

71 

72 

57.50 

43.33 

57.31 

43.58 

57.12 

43.83 

56.93 

44.08 

72 

73 

58.30 

43.93 

58.11 

44.19 

57.91 

44.44 

57.72 

44,69 

73 

74 

59.10 

44.53 

58  .  90 

44.79 

58.71 

45.05 

58,51 

45.30 

74 

75 

59.90 

45.14 

59.70 

45.40 

59.50 

45.66 

59,30 

45.92 

75 

76 

60.70 

45  .  74 

60  .  50 

46.00 

60.29 

46.27 

60,09 

46.53 

76 

77 

61.49 

46.34 

61.29 

46.61 

61.09 

46.87 

60,88 

47.14 

77 

78 

62  .  29 

46.94 

62.09 

47.21 

61.88 

47.48 

61,67 

47.75 

78 

79 

63.09 

47.54 

62.88 

47.82 

62.67 

48.09 

62.46 

48.37 

79 

80 

63.89 

48.15 

63.68 

48.42 

63.47 

48.70 

63.26 

48.98 

80 

81 

64.89 

48  .  75 

64.48 

49.03 

64.26 

49.31 

64,05 

49.59 

81 

82 

65.49 

49.35 

65.27 

49.63 

65.05 

49.92 

64,84 

50,20 

82 

83 

66.29 

49.95 

66.07 

50  .  24 

65.85 

50.53 

65.63 

50.81 

83 

84 

67.09 

50.55 

66.86 

50  .  84 

66.64 

51.14 

66  ,42 

51,43 

84 

85 

67.88 

51.15 

67.66 

51.45 

67.43 

51.74 

67,21 

52.04 

85 

86 

68.68 

51.76 

68.46 

52.06 

68.23 

52.35 

68.00 

52,65 

86 

87 

69.48 

52.36 

69  .  25 

52  .  66 

69.02 

52.96 

68.79 

53  .26 

87 

88 

70.28 

52.96 

70.05 

53  .  27 

69.82 

53  .  57 

69.58 

53,88 

88 

89 

71.08 

53.56 

70.84 

53.87 

70.61 

54.18 

70.37 

54.49 

89 

90 

71.88 

54.16 

71.64 

54  ;48 

71.40 

54.79 

71.16 

55.10 

90 

91 

72.68 

54.77 

72.44 

55  .  08 

72.20 

55.40 

71,95 

55.71 

"  91 

92 

73.47 

55  .  37 

73  .  23 

55  .  69 

72.99 

56.01 

72,74 

56  .  32 

92 

93 

74.27 

55.97 

74.03 

56.29 

73.78 

56.61 

73.53 

56.94 

93 

94 

75.07 

56.57 

74.82 

56  .  90 

74.58 

57.22 

74.32 

57.55 

94 

95 

75.87 

57.17 

75.62 

57.50 

75.37 

57.83 

75.12 

58.16 

95 

96 

76.67 

57.77 

76.42 

58.11 

76.16 

58.44 

75.91 

58.77 

93 

97 

77.47 

58.38 

77.21 

58.71 

76.96 

59.05 

76  .  70 

59.39 

97 

98 

78  .  27 

58,98 

78.01 

59.32 

77.75 

59.66 

77.49 

60.00 

98 

99 

79.06 

59.58 

78.80 

59.92 

78.54 

60.27 

78.28 

60.61 

99 

100 

79.86 

60.18 

79.60 

60.53 

79.34 

60.88 

79.07 

61.22 

100 

| 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

•Lat. 

o* 

o 

a 

1 

m 

1 

s 

53  Deg. 

52|  Deg. 

52£  Deg. 

524  Deg. 

Q 

78 


TBAVHRSE   TABLE. 


o 

38  Deg. 

38*  Deg. 

38i  Deg. 

38|  Deg. 

O 

1 

1" 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

E 

o 
• 

1 

0.79 

0.62 

0.79 

0.62 

0.78 

0.62 

0.78 

0.63 

1 

2 

1.58 

1.23 

1,57 

1.24 

1.57 

1.24 

1.56 

1.25 

2 

3 

2.36 

1.85 

2.36 

1.86 

2.35 

1.87 

2.34 

1.88 

3 

4 

3.15 

2.46 

3.14 

2.48 

3.13 

2.49 

3.12 

2.50 

4 

5 

3.94 

3.08 

3.93 

3.10 

3.91 

3.11 

3.90 

3.13 

5 

G 

4.73 

3.69 

4.71 

3.71 

4.70 

3.74 

4.68 

3.76 

6 

7 

5.52 

4.31 

5.50 

4.33 

5.48 

4.36 

5.46 

4.38 

7 

8 

6.30   4.93 

6.28 

4.95 

6.26 

4.98 

6.24 

5.01 

8 

9 

7.09   5.54 

7.07 

5.57 

7.04 

5.60 

7.02 

5.63 

9 

10 

7.88J  6.16 

7.85 

6.19 

7.83 

6.23 

7.80 

6.26 

10 

11 

:  8.67 

6.77 

8.64 

6.81 

8.61 

6.85 

8.58 

6.89 

11 

12 

9.46 

7.39 

9.42 

7.43 

9.39 

7.47 

9.36 

7.51 

12 

13 

10.24 

8.00 

10.21 

8.05 

10.17 

8.09 

10.14 

8.14 

13 

14 

11.03 

8.62 

10.99 

8.67 

10.96 

8.72 

10.92 

8.76 

14 

15 

11.82 

9.23 

11.78 

9.29 

11.74 

9.34 

11.70 

9.39 

15 

16 

12.61 

9.85 

12.57 

9.91 

12.52 

9.96 

12.48 

10.01 

16 

17 

13.40 

10.47 

13.35 

10.52 

13.30 

10.58 

13.26 

10.64 

17 

.18 

14.18 

11.08 

14.14 

11.14 

14.09 

11.21 

14.04 

11.27 

18 

19 

14.97 

11.70 

14.92 

11.76 

14.87 

11.83 

14.82 

11.89 

19 

20 

15.76 

12.31 

15.71 

12.38 

15.65 

12.45 

15.60 

12.52 

20 

21 

16.55 

12.93 

16.49 

13.00 

16.43 

13.07 

16.38 

13.14 

21 

22 

17.34 

13.54 

17.28 

13.62 

17.22 

13.70 

17.16 

13.77 

22 

23 

18.12 

14.16 

18.06 

14.24 

18.00 

14.32 

17.94 

14.40 

23 

24 

18/91 

14.78 

18.85 

14.86 

18.78 

14.94 

18.72 

15.02 

24 

25 

19.70 

15.39 

19.63 

15.48 

19.57 

15.56 

19.50 

15.65 

25 

26 

20.49 

16.01 

20.42 

16.10 

20  .  35 

16.19 

20.28 

16.27 

26 

27 

21.28 

16.62 

21.20, 

16.72 

21.13 

16.81 

21.06 

16.90 

27 

28 

22.06 

17.24 

21.99 

17.33 

21.91 

17.43 

21.84 

17.53 

28 

29 

22.85 

17.85 

22.77 

17.95 

22.70 

18.05 

22.62 

18.15 

29 

30 

23.64 

18.47 

23  .  56 

18.57 

23.48 

18.68 

23.40 

18.78 

30 

31 

24.43 

19.09 

24.34 

19.19 

24  .  26 

19.30 

24.18 

19.40 

31 

32 

25.22 

19.70 

25.13 

19.81 

25.04 

19.92 

24.96 

20.03 

32 

33 

26.00 

20.32 

25.92 

20.43 

25.83 

20.54 

25.74 

20.66 

33 

34 

26.79 

20  .  93 

26.70 

21.05 

26.61 

21.17 

26.52 

21.28 

34 

35 

27.58 

21.55 

27.49 

21.67 

27.39 

21.79 

27.30 

21.91 

35 

36 

28.37 

22.16 

28.27 

22.29 

28.17 

22.41 

28.08 

22.53 

36 

37 

29.16 

22.78 

29.06 

22.91 

28.96 

23.03 

28.86 

23.16 

37 

38 

29.94 

23.40 

29.84 

23.53 

29.74 

23.66 

29.64 

23.79 

38 

39 

30,73 

24.01 

30.63 

24.14 

30  .  52 

24.28 

30.42 

24.41 

39 

40 

31.52 

24.63 

31.41 

24.76 

31.30 

24.90 

31.20 

25.04 

40 

41 

32.31 

25  .  24 

32.20 

25.38 

32.09 

25.52 

31.98 

25  .  66 

41 

42 

33.10 

25.86 

32  .  98 

26.00 

32.87 

26.15 

32.76 

26.29 

42 

43 

33.88 

26.47 

33.77 

26  .  62 

33.65 

26.77 

33.53 

26.91 

43 

44 

34.67 

27.09 

34.55 

27.24 

34.43 

27.39 

34.31 

27.54 

44 

45 

35.46 

27.70 

35.34 

27,86 

35.22 

28.01 

35.09 

28.17 

45 

46 

36.25 

28.32 

36.12 

28.48 

36.00 

28.64 

35.87 

28.79 

46 

47 

37.04 

28  .  94 

36.91 

29.10 

36.78 

29.26 

36.65 

29.42 

47 

48 

37.82 

29.55 

37.70 

29.72 

37.57 

29.88 

37.43 

30.04 

48 

49 

38.61 

30.17 

38.48 

30.34 

38.35 

30.50 

38.21 

30.67 

49 

50 

39.40 

30.78 

39.27 

30.95 

39.13 

31.13 

38.99 

31.30 

50 

1 

Dep.- 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

I 
Q 

52  Deg. 

51  f  Deg. 

51i  Deg. 

5U  Deg. 

d 
In 

Q 

TRAVERSE   TABLE. 


79 


2 

38  Deg. 

38i  Deg. 

38i  Deg. 

38}  Deg. 

O 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

51 

40.19 

31.40 

40.05 

31.57 

39.91 

31.75 

39.77 

3J.92 

51 

52 

40.98 

32.01 

40.84 

32.19 

40.70 

32.37 

40.55 

32.55 

52 

53 

41.76 

32.63 

41.62 

32.81 

41.48 

32.99 

41.33 

33.17 

53 

54 

42.55 

33.25 

42.41 

33.43 

42.26 

33.62 

42.11 

33.80 

54 

55 

43.34 

33.86 

43.19 

34.05 

43.04 

34.24 

42.89 

34.43 

55 

56 

44.13 

34.48 

43.98 

34.67 

43.83 

34.86 

43.67 

35.05 

56 

57 

44.92 

35.09 

44.76 

35.29 

44.61 

35.48 

44.45 

35.68 

57 

58 

45.70 

35.71 

45.55    35.91 

45.39 

36.11 

45.23 

36.30 

58 

59 

46.49 

36.32 

46.33 

36.53 

46.17 

36.73 

46.01 

36.93 

59 

60 

47.28 

36.94 

47.12 

37.15 

46.96 

37.35 

46.79 

37.56 

60 

61 

48.07 

37.56 

47.90 

37.76 

47.74 

37.97 

47.57 

38.18 

61 

62 

48.86 

38.17 

48.69 

38.38 

48.52 

38.60 

48.35 

38.81 

62 

63 

49.64 

38.79 

49.47 

39.00 

49.30 

39.22 

49.13 

39.43 

63 

64 

50.43 

39.40 

50.26 

39.62 

50.09 

39.84 

49.91 

40.06 

64 

65 

51.22 

40.02 

51.05 

40.24 

50.87 

40.46 

50.69 

40.68 

65 

66 

52.01 

40.63 

51.83 

40.86 

51.65 

41.09 

51.47 

41.31 

66 

67 

52.80 

41.25 

52.62 

41.48 

52.43 

41.71 

52.25 

41.94 

67 

68 

53.58 

41.86 

53.40 

42.10 

53.22 

42.33 

53.03 

42.56 

68 

69 

54.37 

42.48 

54.19 

42.72 

54.00 

42.95 

53.81 

43.19 

69 

70 

55.16 

43.10 

54.97 

43.34 

54.78 

43.58 

54.59 

43.81 

70 

71 

55  .  95 

43.71 

55.76 

43.96 

55.57 

44.20 

55.37 

44.44 

71 

72 

56.74 

44.33 

56.54 

44.57 

56.35 

44.82 

56.15 

45.07 

72 

73 

57.52 

44.94 

57.33 

45.19 

57.13 

45.44 

56.93- 

45.69 

73 

74 

58.31 

45,56 

58.11 

45.81 

57.91 

46.07 

57.71 

46.32 

74 

TO 

59.10 

4^.17 

58.00 

46.48 

58.70 

46.69 

58.49 

46.94 

75 

76 

59.89 

46.79 

59.68 

47.05 

59.48 

47.31 

59.27 

47.57 

76 

77 

60.68 

47.41 

60.47 

47.67 

60.26 

47.93 

60.05 

48.20 

77 

78 

61.46 

48.02 

61.25 

48.29 

61.04 

48.56 

60.83 

48.82 

78 

79 

62.25 

48.64 

62.04 

48.91 

61.83 

49.18 

61.61 

49.45 

79 

80 

63.04 

49,25 

62.83 

49.53 

62.61 

49.80 

62.39 

50.07 

80 

81 

63.83 

49.87 

63.61 

50.15 

63.39 

50,42 

63.17 

50.70 

81 

82 

64.62 

50.48 

64.40 

50.77 

64.17 

51.05 

63.95 

51.33 

82 

83 

65.40 

51,10 

65.18 

51.38 

64.96 

51.67 

64.73 

51.95 

83 

84 

66.19 

51.72 

65.97 

52.00 

65.74 

52.29 

65.51 

52.58 

84 

85 

66.98 

52.33 

66.75 

52.62 

66.52 

52.91 

66.29 

53.20 

85 

86 

67.77 

52.95 

67.54 

53.^4 

67.30 

53.54 

67.07 

53.83 

86 

87 

68.56 

53.56 

68.32 

53.86 

68.09 

54.16 

67,85 

54.46 

87 

88 

69.34 

54.18 

6.0  .  1  1 

54.48 

68.87 

54,78 

68.63 

55.08 

88 

89 

70.13 

54.79 

69.89 

55.10 

69.65 

55.40 

69.41 

55.71 

89 

90 

70.92 

55.41 

70.68 

55  .  72 

70.43 

56.03 

70.19 

56.33 

90 

91 

71.71 

56.03 

71,46 

56.34! 

71.22 

56  .  65 

70.97 

50.96 

91 

92 

72.50 

56.64 

72,25 

56  .  96 

72.00 

57.27 

71.75 

57.58 

92 

93 

73.28 

57,26 

73.03 

57.58  ; 

72.78 

57.89 

72.53 

58.21 

93 

94 

74.07 

57.87 

73.82 

58.19 

73.57 

58.52 

73.31 

58.84 

94 

95 

74.86 

58.49 

74.61 

58.81     74.35 

59.14 

74,09 

59.46 

95 

96 

75.65 

59.10 

75.39 

59.43 

75.13 

59.76 

74,8-7 

60,09 

96 

97 

76.44 

59.72 

76.18 

60.05 

75,91 

60.33 

75.65 

60,71 

97 

98 

77.22 

60.33 

76.96 

60.67 

76.70 

61.01 

76.43 

61.34 

98 

99 

78.01 

60.95 

77.75 

61.29 

77.48 

61.63 

77.21 

61.  97 

99 

100 

78.80 

61.57 

78.53 

61.91 

78.26 

62.25 

77.99 

62.59 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

La,t. 

Dep. 

Lat. 

I 

1 

52  Deg. 

51|  Deg. 

51  i  Deg. 

5H  Deg. 

Q 

TRAVERSE    TABLE, 


G 

39  Deg. 

39i  Deg. 

39£  Deg. 

39f  Deg. 

s- 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1 

0.78 

0.63 

0.77 

0.63 

0.77 

0.64 

0.77 

0.64 

1 

2 

1.55 

1.26 

1.55 

1.27 

1.54 

1.27 

1.54 

1.28 

3 

2.33 

1.89 

2.32 

1.90 

2.31 

1.91 

2.31 

1.92 

j 

4 

3.11 

2.52 

3.10 

2.53 

3.09 

2.54 

3.08 

2.56 

4 

5 

3.89 

3.15 

3.87 

3.16 

3.86 

3.18 

3.84 

3.20 

5 

6 

4.66 

3.78 

4.65 

3.80 

4.63 

3.82 

4.61 

3.84 

6 

7 

5.44 

4.41 

5.42 

4.43 

5.40 

4.45 

5.38 

4.48 

7 

8 

6.22 

5.03 

6.20 

5.06 

6.17 

5.09 

6.15 

5.12 

8 

9 

6.99 

5.66 

6.97 

5.69 

6.94 

5.72 

6.92 

5.75 

9 

10 

7.77 

6.29 

7.74 

6.33 

7.72 

6.36 

7.69 

6.39 

10 

11 

8.55 

6.92 

8.52 

6.96 

8.49 

7.00 

8.46 

7.03 

11 

12 

9.33 

7.55 

9.29 

7.59 

9.26 

,7.63 

9.23 

7.67 

12 

13 

10.10 

8.18 

10.07 

8.23 

10.03 

£.27 

9.99 

8.31 

13 

14 

10.88 

8.81 

10.84 

8.86 

10.80 

8.91 

10.76 

8.95 

14 

15 

11.66 

9.44 

11.62 

9.49 

11.57 

9.54 

11.53 

9.59 

15 

16 

12.43  10.07 

12.39 

10.12 

12.35 

10.18 

12.30 

10.23 

16 

•  17 

13.21 

10.70 

13.16 

10.76 

13.12 

10.81 

13.07 

10.87 

17 

18 

13.99 

11.33 

13.94 

11.39 

13.89 

11.45 

13.84 

11.51 

18 

19 

14.77 

11.96 

14.71 

12.02 

14.66 

12.09 

14.61 

12.15 

19 

20 

15.54 

12.59 

15.49 

12.65 

15.43 

12.72 

15.38 

12.79 

20 

21 

16.32 

13.22 

16.26 

13.29 

16.20 

13.36 

16.15 

13.43 

21 

22 

17.10 

13.84 

17.04 

13.92 

16.98 

13.99 

16.91 

14.07 

22 

23 

17.87 

14.47 

17.81 

14.55 

17.75 

14.63 

17.68 

14.71 

23 

24 

18.65 

15.10 

18.59 

15.18 

18.52 

15.27 

18.45 

15,35 

24 

20 

19.43 

15.73 

19.36 

15.82 

19.29 

15.90 

19.22 

15.99 

25 

26 

20.21 

16.36 

20.13 

16.45 

20.06 

16.54 

19.99 

10.63 

26 

27 

20.98 

16.99 

20.91 

17.08 

20.83 

17.17 

20.76 

17.26 

27 

28 

21.76 

17.62 

21.68 

17.72 

21.61 

17.81 

21.53 

17.90 

28 

29 

22.54 

18.25 

22.46 

18.35 

22.38 

18.45 

22.30 

18.54" 

29 

30 

23.31 

18.88 

23.23 

18.98 

23.15 

19.08 

23.07 

19.18 

30 

31 

24.09 

19.51 

24.01 

19.61 

23.92 

19.72 

23.83 

19.82 

31 

32 

24.87 

20.14 

24.78 

20.25 

24.69 

20.35 

24.60 

20.46 

32 

33  25.65 

20.77 

25.55 

20.88 

25  .  46 

20.99 

25.37 

21.10 

33 

34 

26.42 

21.40 

26.33 

21.51 

26.24 

21.63 

26.14 

21.74 

34 

35 

27.20 

22.03 

27.10 

22.14 

27.01 

22.26 

26.91 

22.38 

35 

36  27.98 

22.66 

27.88 

22.78 

27.78 

22.90 

27.68 

23.02 

36 

37  |  28.75 

23.28 

28.65 

23.41 

28  .  55 

23.53 

28.45 

23.66 

37 

38 

29  .  53 

23.91 

29.43 

24.04 

29.32 

24.17 

29.22 

24.30 

38 

39 

30.31  24.54 

30  .  20 

24.68 

30.09 

24.81 

29.98 

24.94 

39 

40 

31.09  125.17 

30.98 

25.31 

30.86 

25.44 

30.75 

25  .  58 

40 

41 

31.86 

25.80 

31.75 

25  .  94 

31.64 

26.08 

31.52 

26  .  22 

41 

42 

32.64 

26.43 

32  .  52 

26.57 

32.41 

26.72 

32.29 

26.86 

42 

43 

33.42 

27.06 

33.30 

27.21 

33.18 

27.35 

33.06 

27.50 

43 

44 

34.19 

27.69 

34.07 

27.84 

33.95 

27.99 

33.83 

28.14 

44 

45 

34.97 

28  .  32 

34.85 

28.47 

34.72 

28.62 

34.60 

28.77 

45 

46 

35.75 

28.95 

35  .  62 

29.10 

35.49 

29.26 

35.37 

29.41 

46 

47 

36.53 

29.58 

36.40 

29  .  74 

36  .  27 

29.90 

36.14 

30.05 

47 

48 

37.30 

30.21 

37.17 

30.37 

37.04 

30.53 

36.90 

30.69 

48 

49 

38.08 

30.84  37.95 

31.00 

37.81 

31.17 

37.67 

31.33 

49 

50 

38.86 

31.47  38.72 

31.64 

38.58 

31.80 

38.44 

31.97 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

0 

o 

a 

• 

2 

51  Deg. 

50|  Deg. 

50  i  Deg. 

5(H  Deg. 

Q 

TRAVERSE    TABLE. 


o 

? 

39  Deg. 

39}  Deg. 

39  £  Deg. 

39|  Deg. 

O 

a 
o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 
n 

CD 

"61 

39.63 

32.10 

39.49 

32.27 

39.35 

32.44 

39.21 

32.61 

~5~T 

52 

40.41 

32.72 

40.27 

32.90 

40.12 

33.08 

39.98 

33.25 

52 

53 

41.19 

33.35 

41.04 

33.53 

40.90 

33.71 

40  .  75 

33.89 

53 

54 

41.97 

33.98 

41.82 

34,17 

41.67 

34.35 

41.52 

34.53 

54 

5o 

42.74 

34.61 

42.59 

34.80 

42.44 

34.98 

42.29 

35.17 

55 

56 

43.52 

35.24 

43.37 

35.43 

43.21 

35  .  62 

43.06 

35.81 

56 

57 

44.30 

35.87 

44.14 

36.06 

43.98 

36.26 

43.82 

36.45 

57 

58 

45.07 

36.50 

44.91 

36.70 

44.75 

36.89 

44.59 

37.09 

58 

59 

45.85 

37.13 

45.69 

?7.33 

45.53 

37.53 

45.36 

37.73 

59 

60 

48.63 

37.76 

46.46 

37.96 

46.30 

38.16 

46.13 

38.37 

60 

61 

47.41 

38.39 

47.24 

38  .  60 

47.07 

38.80 

46.90 

39.01 

61 

62 

48.18 

39.02 

48.01 

39.23 

47.84 

39.44 

47.67 

39.65 

62 

63 

48.96 

39.65 

48.79 

39.86 

48.61 

40.07 

48.44 

40.28 

63 

64 

49.74 

40  .  28 

49.56 

40.49 

49.38 

40.71 

49.21 

40.92 

64 

65 

50.51 

40.91 

50.34 

41.13 

50.16 

41.35 

49.97 

41.56 

65 

66 

51.29 

41.54 

51.11 

41.76 

50.93 

41.98 

50.74 

42.20 

66 

67 

52.07 

42.16 

51.88 

42.39 

51.70 

42  .  62 

51.51 

42.84 

67 

68 

52.85 

42.79 

52.66 

43.02 

52.47 

43.25 

52.28 

43.48 

68 

69 

53.52 

43.42 

53.43 

43.66 

53  .  24 

43.89 

53.05 

44.12 

69 

70 

54.40 

44.05 

54.21 

44.29 

54.01 

44.53 

53.82 

44.76 

70 

71 

55.18 

44  .  68  1 

54.98 

44.92 

54.79 

45.16 

54.59 

45.40 

71 

72 

55.95 

45.31 

55.76 

45  .  55 

55  .  56 

45.80 

55.36 

46.04 

72 

73 

56  .  73 

45.94 

56.53 

46.19 

56.33 

46.43 

56.13 

46.68 

73 

74 

57.51 

46.57 

57.31 

46.82 

57.10 

47.07 

56.89 

47.32 

74 

75 

58.29 

47.20 

58.08 

47.45 

57.87 

47.71 

57.66 

47.96 

75 

76 

59.06 

47.83 

58.85 

48.09 

58.64 

48.34 

58.43 

48.60 

76 

77 

59.84 

48.46 

59.63 

48.72 

59.42 

48.98 

59.20 

49.24 

77 

78 

60.62 

49.09 

60.40 

49.35 

60.19 

49.61 

59.97 

49.88 

78 

79 

61.39 

49.72 

61.18 

49  .  98 

60.96 

50.25 

60.74 

50.52 

79 

80 

62.17 

50  .  35 

61.95 

50.62 

61.73 

50.89 

61.51 

51.16 

80 

81 

62.95 

50.97 

62.73 

51.25 

62\  50 

51.52 

62.28 

51.79 

81 

82 

63  .  73 

51.60 

63  .  50 

51.88 

63  .  27 

52.16 

63.04 

52.43 

82 

83 

64.50 

52  .  23 

64.27 

52.51 

64.04 

52  .  79 

63.81 

53.07 

83 

84 

65  .  28 

52.86 

65.05 

53.15 

64.82 

53.43 

64.58 

53.71 

84 

85 

66.06 

53.49 

65.82 

53.78 

65.59 

54.07 

65.35 

54.35 

85 

86 

66.83 

54.12 

66.60 

54.41 

66.36 

54.70 

66.12 

54.99 

86 

87 

67.61 

54.75 

67.37 

55.05 

67.13 

55.34 

66.89 

55  .  63 

87 

88 

68.39 

55  .  38 

68.15 

55  .  68 

67.90 

55.97 

67.66 

56.27 

88 

89 

69.17 

56.01 

68.92 

56.32 

68.67 

56.61 

68.43 

56.91 

89 

90 

69.94 

56.64 

69  .  70 

56.94 

69.45 

57.25 

69.20 

57.55 

90 

91 

70.72 

57.27 

70.47 

57.58 

70.22 

57.88 

69.96 

58.19 

91 

92 

71.50 

57.90 

71.24 

58.21 

70.99 

58.52 

70  .  73 

58.83 

92 

93 

72  .  27 

58  .  53 

72.02 

58.84 

71.76 

59.16 

71.50 

59.47 

93 

94 

73.05 

59.16 

72  .  79 

59.47 

72.53 

59.79 

72.27 

60.11 

94 

95 

73.83 

59.79 

73.57 

60.11 

73.30 

60.43 

73.04 

60  .  75 

95 

96 

74.61 

60.41 

74.34 

60.74 

74.08 

61.06 

73.81 

61.39 

96 

97 

75.38 

61.04 

75.12 

61.37, 

74.85 

61.70 

74.58 

62.03 

97 

98 

76.16 

61.67 

75.89 

62.01 

75.62 

62.34 

75.35 

62.66 

98 

99 

76.94 

62.30 

76.66 

62.64 

76.39 

62.97 

76.12 

63.30 

99 

100 

77.71 

62.93 

77.44 

63.27 

77.16 

63.61 

76.88 

63.94 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

In 

3 

51  Deg. 

50|  Deg. 

50i  Deg. 

50i  Deg. 

3 

TRAVERSE    TABLE. 


G 

40  Deg. 

40}  Deg. 

40i  Deg. 

40|  Deg. 

1 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep, 

s 

1 

0.77 

0.64 

0.76 

0.65 

0.76 

0.65 

0.76 

0.65 

1 

2 

1.53 

1.29 

1.53 

1.29 

1.52 

1.30 

1.52 

1.31 

2 

3 

2.30 

1,93 

2.29 

1.94 

2.28 

1.95 

2.27 

1.96 

3 

4 

3.06 

2.57 

3.05 

2.58 

3.04 

2.60 

3.03 

2.61 

4 

5 

3.83 

3.21 

3.82 

3.23 

3.80 

3.25 

3  .  79 

3.26 

5 

6 

4.60 

3.86 

4.58 

3.88 

4.56 

3.90 

4.55 

3.92 

6 

7 

5.36 

4.50 

5.34 

4.52 

5.32 

4.55 

5.30 

4.57 

7 

8 

6.13 

5.14 

6.11 

5.17 

6.08 

5.20 

6.06 

5.22 

8 

9 

6.89 

5.79 

6.87 

5.82 

6.84 

5.84 

6.82 

5.87 

9 

10 

7.66 

6.43 

7.63 

6.46 

7.60 

6.49 

7.58 

6.53 

10 

11 

8.43 

7.07 

8.40 

7.11 

8.36 

7.14 

8.33 

7.18 

11 

12 

9.19 

7.71 

9.16 

7.75 

9.12 

7.79 

9.09 

7.83 

12 

13 

9.96 

8.36 

9.92 

8.40 

9.89 

8.44 

9.85 

8.49 

13 

14 

10.72 

9.00 

10.69 

9.05 

10.65 

9.09 

10.61 

9.14 

14 

15 

11.49 

9.64 

11.45 

9.69 

11.41 

9.74 

11.36 

9.79 

15 

16 

12.26 

10.28 

12.21 

10.34 

12.17 

10.39 

12.12 

10.44 

16 

17 

13.02 

10.93 

12.97 

10.98 

12.93 

11.04 

12.88 

11.10 

17 

18 

13.79 

11.57 

13.74 

11.63 

13.69 

11.69 

13,64 

11.75 

18 

19 

14.55 

12.21 

14.50 

12.28 

14.45 

12.34 

14.39 

12.40 

19 

20 

15.32 

12.86 

15.26 

12.92 

15.21 

12.99 

15.15 

13.06 

20 

21 

16.09 

13.50 

16.03 

13.57 

15.97 

13.64 

15.91 

13.71 

21 

22 

16.85 

14.14 

16.79 

14.21 

16.73 

14.29 

16.67 

14.36 

22 

23 

17.62 

14.78 

17.55 

14.86 

17.49 

14.94 

17.42 

15.01 

23 

24 

18.39 

15.43 

18.32 

15.51 

18.25 

15.59 

18.18 

15.67 

24 

25 

19.15 

16.07 

19.08 

16.15 

19.01 

16.24 

18.94 

16.32 

25 

26 

19.92 

16.71 

19.84 

16.80 

19.77 

16.89 

19.70 

16.97 

26 

27 

20.68 

17.36 

20.61 

17.45 

20.53 

17.54 

20.45 

17.62 

27 

28 

21.45 

18.00 

21.37 

18.09 

21.29 

18.18 

21.21 

18.28 

28 

29 

22.22 

18.64 

22.13 

18.74 

22.05 

18.83 

21.97 

18.93 

29 

30 

22.98 

19.28 

22.90 

19.38 

22.81 

19.48 

22.73 

19.58 

30 

31 

23  .  75 

19.93 

23.66 

20.03 

23.57 

20.13 

23.48 

20.24     31 

32 

24.51 

20.57 

24.42 

20.68 

24.33 

20.78 

24.24 

20.89 

32 

33 

25.28 

21.21 

25.19 

21.32 

25.09 

21.43 

25.00 

21.54 

33 

34 

26.05 

21.85 

25.95 

21.97 

25.85 

22.08 

25.76 

22.19 

34 

35 

26.81 

22.50 

26.71 

22.61 

26.61 

22.73 

26.51 

22.85 

35 

36 

27.58 

23.14 

27.48 

23.26 

27.37 

23.38 

27.27 

23  .  50 

36 

37 

28.34 

23.78 

28.24 

23.91 

28.13 

24.03 

28.03 

24.15 

37 

38 

29  .  1  1 

24.43 

29.00 

24.55 

28.90 

24.68 

28.79 

24.80 

38 

39 

29.88 

25.07 

29.77 

25.20 

29.66 

25  .  33 

29.54 

25.46 

39 

40 

30.64 

25.71 

30.53 

25.84 

30.42 

25.98 

30.30 

-26.11 

40 

41 

31.41 

26.35 

31.29 

26.49 

31.18 

26.03 

31.06 

26.76 

41 

42 

32.17 

27.00 

32.06 

27.14 

31.94 

27.28 

31.82 

27.42 

42 

43 

32.94 

27.64 

32.82 

27.78 

32.70 

27.93 

32.58 

28.07 

43 

44 

33.71 

28.28 

33.58 

28.43 

33.46 

28.58 

33.33 

28.72 

44 

45 

34.47 

28.93 

34.35 

29.08 

34.22 

29.23 

34.09 

29.37 

45 

46 

35.24 

29.57 

35.11 

29.72 

34.98 

29.87 

34.85 

30.03 

46 

47 

36.00 

30.21 

35.87 

30.37 

35.74 

30.52 

35.61 

30.68 

47 

48 

36.77 

30.85 

36.64 

31.01 

36.50 

31.17 

36.36 

31.33 

48 

49 

37.54 

31.50 

37.40 

31.66 

37.26 

31.82 

37.12 

31.99 

49 

50 

38.30 

32.14 

38.16 

32.31 

38.02 

32.47 

37.88 

32  .  64 

50 

o> 
o 
PS 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

1 

Q 

50  Deg. 

49|  Deg. 

49i  Deg. 

494  Deg. 

td 

To 

o 

TRAVERSE    TABLE. 


03 


g 

33' 

40  Deg, 

40  i  Deg. 

40^  Deg. 

40£  Deg. 

O 

n 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

Lat. 

Dep. 

I 

51 

39  .  07 

32.78 

38  .  92 

32.95 

38  .  78 

33.12 

3*.  64 

33.29 

51 

52 

39.83 

33,42 

39,69 

33.60 

39.54 

33.77 

39.39 

33,94 

52 

53 

40.60 

34.07 

40.45 

34.^4 

40.30 

34.42 

40.15 

34.60 

53 

54 

41.37 

34.71 

41.21 

34.89 

41.06 

35.07 

40.91 

35.25 

54 

55 

42.13 

35.35 

41.98 

35  .  54 

41.82 

35.72 

41.67 

35.90 

55 

56 

42.90 

36.00 

42.74 

36.18 

42.58 

36.37 

42,42 

36,55 

56 

57 

43,66 

36  .  64 

43.50 

36.83 

43.34 

37.02 

43.18 

37,21 

57 

58 

44.43 

37.28 

44.27 

37.48 

44.10 

37.67 

43.94 

37.86 

58 

59 

45.20 

37.92 

45.03 

38.12 

44.86 

38.32 

44.70 

38.51 

59 

60 

45.96 

38.57 

45  .  79 

38  .  77 

45.62 

38.97 

45.45 

39.17 

60 

81 

46.73 

39.21 

46.56 

39.41 

46.38 

39.62 

46.21 

39.82 

e: 

62 

47.49 

39.85 

47.32 

40.06 

47.15 

40.27 

46.97 

40.47 

62 

63 

48.26 

40.50 

48.08 

40.71 

47.91 

40.92 

47.73 

41.12 

63 

64 

49.03 

41,14 

48.85 

41.35 

48.67 

41.56 

48.48 

41.78 

64 

65 

49,79 

41,78 

49.61 

42.00 

49.43 

42.21 

49.24 

42.43 

65 

66 

50  .  56 

42.42 

50.37 

42.64 

50.19 

42.86 

50.00 

43.08 

66 

67 

51.32 

43.07 

51.14 

43.29 

50.95 

43,51 

50.76 

43.73 

67 

68 

52.09 

43.71 

51.90 

43.94 

51.71 

44.16 

51.51 

44.39 

68 

69 

52.86 

44.35 

52.66 

44.58 

52.47 

44.81 

52.27 

45.04 

69 

70 

53  .  62 

45  .  00 

53.43 

45.23 

53.23 

45.46 

53.03 

45.69 

70 

71 

54,39 

45.64 

54.19 

45.87 

53.99 

46.11 

53.79 

46.35 

71 

73' 

55.16 

46.28 

54.95 

46.52 

54.75 

46.76 

54.54 

47.00 

72 

73 

55.92 

46,92 

55.72 

47.17 

55.51 

47.41 

55.30 

47.65 

73 

74 

56  .  69 

47.57 

56.48 

47.81 

56.27 

48.06  i 

56.06 

48.30 

74 

75 

57.45 

48.21 

57.24 

48.46 

57.03 

48.71 

56.82 

48.96 

75 

76 

58.22 

48.85 

58.01 

49.11 

57.79 

49.36 

57.57 

49.61 

76 

77 

58.99 

49.49 

58,77 

49.75 

58.55 

50.01 

58.33 

50.26 

77 

78 

59.75 

50.14 

59.53 

50.40 

59.31 

50,66 

59.09 

50.92 

78 

79 

60.52 

50.78 

60.30 

51.04 

60.07 

51.31 

59.85 

51.57 

79 

80 

6  1  .  28 

51.42 

61.06 

51.69 

60.83 

51.96 

60.61 

52.22 

80 

8i 

62.05 

52.07 

61.82 

52.34 

61.59 

52.61 

61.36 

52.87 

81 

82 

62.82 

52.71 

62.59 

52.98 

62.35 

53.25 

62.12 

53  .  53 

82 

83 

63.58 

53.35 

63.35 

53.63 

63.11 

53.90 

62.88 

54.18 

83 

84 

64.35 

53.99 

64.11 

54.27 

63.87 

54.55 

63.64 

54.83 

84 

85 

65  .  1  i 

54.64 

64.87 

54.92 

64.63 

55,20 

64.39 

55.48 

85 

86 

65.88 

55.28 

65.64 

55,57 

65.39 

55.85 

65.15 

56.14 

86 

87 

66.65 

55.92 

66.40 

56.21 

66.16 

56.50 

65.91 

56.79 

87 

88 

67.41 

56  .  57 

67.16 

56.86 

66.92 

57.15 

66.67 

57.44 

88 

89 

68,18 

57.21 

67.93 

57.50 

67.68 

57.80 

67.42 

58.10 

89 

68.94 

57.85 

68.69 

58.15 

68.44 

58.45 

68.18 

58  .  75 

90 

~9l 

69.71 

58.49 

69,45 

58.80i 

69.20 

59.10 

68.94 

59.40 

91 

92 

70  .  48 

59.14 

70.22 

59.44 

69.96 

59.75 

69.70 

60.05 

92 

93 

71.24 

59,78 

70.98 

60,09 

70.72 

60.40 

70.45 

60.71 

93 

94 

72.01 

60.42 

71.74 

60.74 

71,48 

61.05 

71.21 

61.36 

94 

95 

72,77 

61.06 

72.51 

61.38 

72.24 

61.70 

71.97 

62.01 

95 

96 

73  .  54 

61.71 

73.27 

62.03 

73.00 

62.35 

72.73 

62.66 

96 

97 

74  .  3  1 

62  .  35 

74,03 

62.67 

73.76 

63.00 

73.48 

63.32 

97 

98 

75  .  07 

62.99 

74.80 

03.32 

74.52 

63.65 

74;  24 

63.97 

98 

99 

75.84 

63.64 

75.56 

63.97 

75.28 

64.30 

75.00 

64.62 

99 

100 

64.28 

76.32 

64.61 

76.04 

64.94 

75.76 

65.28 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

.2 
Q 

50  Deg. 

491  Deg. 

49  i  Deg. 

49$  Deg. 

.2 

Q 

n 


84 


TRAVERSE    TABLE. 


5' 

s 

41  Deg. 

41}  Deg. 

41!  DeS- 

41|  Deg. 

O 
55' 

B 

C5 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

1 

0.75 

0.6G 

0.75 

~07C6~ 

0.75 

0.66 

0.75 

0.67 

1 

2 

1.51 

1.31 

1.50 

1.32 

1.50 

1.33 

1.49 

1.33 

2 

3 

2.26 

1.97 

2.26 

1.98 

2.25 

1.99 

2.24 

2.00 

3 

4 

3.02 

2.62 

3.01 

2.64 

3.00 

2.65 

2.98 

2.66 

4 

5 

3.77 

3.28 

3.76 

3.30 

3.74 

3.31 

3.73 

3.33 

5 

6 

4.53 

3.94 

4.51 

3.96 

4.49 

3.98 

4.48 

4.00 

6 

7 

5.29 

4.59 

5.26 

4.62 

5.24 

4.64 

5.22 

4.66 

7 

8 

6.04 

5.25 

6.01 

5.27 

5.99 

5.30 

5.97 

5.33 

8 

9 

6.79 

5.90 

6.77 

5.93 

6.74 

5.SK3 

6.71 

5,99 

9 

10 

7.55 

6.56 

7.52 

6.59 

7.49 

6.63 

7.46 

6.66 

10 

11 

8.30 

7.22 

8.27 

7.25 

8.24 

7.29 

8.21 

7.32 

11 

12 

9.06 

7.87 

9.02 

7.91 

8.99 

7.95 

8.95 

7.99 

12 

13 

9.81 

8.53 

9.77 

8.57 

9.74 

8.61 

9.70 

8.66 

13 

14 

10.57 

9.18 

10.53 

9.23 

10.49 

9.28 

10.44 

9.32 

14 

15 

11.32 

9.84 

11.28 

9.89 

11.23 

9.94 

11.19 

9.99 

15 

16 

12.08 

10.50 

12.03 

10.55 

11.98 

10.60 

11.94 

10.65 

16 

17  12.83 

11.15 

12.78 

11.21 

12.73 

11.26 

12.68 

11.32 

17 

18 

13.58 

11.81 

13.53 

11.87 

13.48 

11.93 

13.43 

11.99 

18 

19 

14.34 

12.47 

14.28 

12.53 

14.23 

12.59 

14.18 

12.65 

19 

20 

15.09 

13.12 

15.04 

13.19 

14.98 

13.25 

14.92 

13.32 

20 

21 

15.85 

13.78 

15.79 

13.85 

15.73 

13.91 

15.67 

13.98 

21 

22 

16  .  60 

14.43 

16.54 

14.51 

16.48 

14.58 

16.41 

14.65 

22 

23 

17.36 

15.09 

17.29 

15.16 

17.23 

15.24 

17.16 

15.32 

23 

24 

18.11 

15.75 

18.04 

15.82 

17.97 

15.90 

17.91 

15.98 

24 

25 

18.87 

16.40 

18.80 

16.48 

18.72 

16.57 

18.65 

16.65 

25 

26 

19.62 

17.06 

19.55 

17.14 

19.47 

17.23 

19.40 

17.31 

26 

27 

20.38  1  17.71 

20.30 

17.80 

20  .  22 

17.89 

20.14 

17.98 

27 

28 

21.13  18.37 

21.05 

18.46 

20.97 

18.55 

20.89 

18.64 

28 

29 

21.89  !  19.03 

21.80 

19.12 

21.72 

19.22 

21.64 

19.31 

29 

30 

22.64  '!  19.68 

22.56 

19.78 

22.47 

19.88 

22.38 

19.98 

30 

31 

23.40  20.34 

23.31 

20.44 

23.22 

20.54 

23.13 

20.64 

31 

32 

24.15  '20.99 

24.06 

21.10 

23.97 

21.20 

23.87 

21.31 

32 

33 

24.91  !21.65 

24.81 

21.76 

24.72 

21.87 

24.62 

21.97 

33 

34 

25.66  22.31 

25.56 

22.42 

25.46 

22.53 

25.37 

22.64 

34 

35 

26.41  22.96 

26.31 

23.08 

26.21 

23.19 

26.1] 

23.31 

35 

36 

27.17  23.62 

27.07 

23.74 

26.96 

23.85 

26.86 

23.97 

36 

37 

27.92  124.27 

27.82 

24.40 

27.71 

24.52 

27.60 

24  .  64 

37 

38 

28.68  !24.93 

28.57 

25.06 

28.46 

25.18 

28.35 

25.30 

38 

39 

29.43  i25.59 

29.32 

25.71 

29.21 

25.84 

29.10 

25.97 

39 

40 

30.19  126.24 

30.07 

26.37 

29.96 

26.50 

29.84 

26.64 

40 

41 

30.94  '26.90  1  30.83 

27.03 

30.71 

27.17 

30.59 

27.30 

41 

42 

31.70  27.55 

31.58 

27.69 

31.46 

27.83 

31.33 

27.97 

42 

43 

32.45  ;28.21 

32.33 

28.35 

32.21 

28.49 

32.08 

28.63 

43 

44 

33.21  ,28.87 

33.08 

29.01 

32.95 

29.16 

32.83 

29.30 

44 

'  45 

33.96  J29.52 

33.83 

29.67 

33  .  70 

29.82 

33.57 

29.97 

45 

46 

34.72  30.18 

34.58 

30.33 

34.45 

30.48 

34.32 

30  .  63 

46 

47 

35.47  30.83 

35.34 

30.99 

35.20 

31.14 

35.06 

31.30 

47 

48 

36.23  31.49 

36.09 

31.65 

35.95 

31.81 

35.81 

31.96 

48 

49 

36.98 

32.15 

36.84 

32.31 

36.70 

32.47 

36.56 

32.63 

49 

50 

37.74 

32.80 

37.59 

32.97 

37.45 

33.13 

37.30 

33.29 

50 

8 

Dep.  I  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

8 

1 

1 

n 

.2 

5 

49  Deg. 

48£  Deg. 

48i  Deg. 

48±  Deg. 

s 

TRAVERSE    TABLE. 


85 


a 

41  Deg. 

4U  Deg. 

41i  Deg. 

41|  Deg. 

O 

p 

1 

3 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

,51 

38.49 

33.46 

38.34 

33.63 

38.20 

33.79 

38.05 

33  .  96 

51 

52 

39  .  24 

34.12 

39.10 

34.29 

38  .  95 

34.46 

38  .  79 

34.63 

52 

53 

40.00 

34.77 

39.85 

34.95 

39  .  69 

35.12 

39.54 

35.29 

53 

54 

40.75 

35.43 

40.60 

35  .  60 

40.44 

35.78 

40.29 

35  .  96 

54 

55  41.51 

36.08 

41.35 

36.26 

41.19 

36.44 

41.03 

36  .  62 

55 

56 

42.26 

36.74 

42.10 

36.92 

41.94 

37.11 

41.78 

37.29 

56 

57 

43.02 

37.40 

42.85 

37.58 

42.69 

37.77 

42.53 

37.96 

57 

58 

43  .  77 

38  .  05 

43.61 

38.24 

43.44 

38.43 

43.27 

38  .  62 

58 

59 

44.53 

38.71 

44.36 

38.90 

44.19 

39.09 

44.02 

39.29 

59 

60 

45.28 

39  .  36 

45.11 

39  .  56 

44.94 

39  .  76 

44.76 

39  .  95 

60 

61 

46.04 

l  40  .  02 

45.86 

40.22 

45  .  69 

40.42 

45.51 

40  .  62 

61 

62 

46.79 

40.68 

46.61 

40.88 

46.44 

41.08 

46  .  26 

41.28 

62 

63 

47.55 

41.33 

47.37 

41.54 

47.18 

4  1  .  75 

47.00 

41.95 

63 

64 

48.30 

41.99 

48.12 

42  .  20 

47.93 

42.41 

47.75 

42  .  62 

64 

65 

49.06 

42.64 

48.87 

42.86 

48.68 

43.07 

48.49 

43  .  28 

65 

66 

49.81 

43.30 

49.62 

43.52 

49.43 

43.73 

49  .  24 

43  .  95 

66 

67 

50.57 

43.96 

50.37 

44.18 

50.18 

44.40 

49.99 

44.61 

67 

68 

51.32 

44.61 

51.13 

44.84 

50.93 

45.06 

50.73 

45  .  28 

68 

69 

52.07 

45.27 

51.88 

45.49 

51.68 

45  .  72 

51.48 

45.95 

69 

70 

52.83 

45.92 

52.63 

46  .  1  5 

52.43 

46.38 

52.22 

46.61 

70 

71 

53.58 

46.58 

53.38 

46.81 

53.18 

47  .  05 

52.97 

47.28  |  71 

72 

54.34 

47.24 

54.  i  3 

47.47 

53  .  92 

47.71 

53.72 

47.94 

72 

73 

55.09 

47.89 

54.88 

48.13 

54.67 

48.37 

54.46 

48.61 

73 

74 

55.85 

48.55 

55.64 

48.79 

5f5.42 

49.03 

55.21 

49.28 

74 

75 

56.60 

49.20 

56.39 

49.45 

56.17 

49.70 

55  .  95 

49.94 

75 

76 

57.36 

49.86 

57.14 

50.11 

56.92 

50.36 

56.70 

50.61 

76 

77 

58  .  1  1 

50.52 

57.89 

50  .  77 

57.67  51.02 

57.45 

51.27 

77 

78 

58.87 

51.17 

58  .  64 

51.43 

58.42 

51.68 

58.19 

51.94 

78 

79 

59.62 

51.83 

59.40 

52.09 

59.17 

52.35 

58.94 

52.60 

79 

80 

60.38 

52.48 

60.15 

52  .  75 

59.92 

53.01 

59.68 

53  .  27 

80 

81 

61.13 

53.14 

60.90 

53.41  1 

60  .  67 

53.67 

60.43 

53.94 

81 

82 

61.89 

53  .  80 

61.65 

54.07 

61.41 

54.33 

61.18 

54.60 

82 

83 

62.64 

54.45 

62.40 

54.73 

62.16 

55.00 

61.92 

55.27 

83 

84 

63.40 

55  .  1  1 

63.15 

55  .  38 

62.91 

55.66 

62.67 

55.93 

84 

85 

64.  15  I  55.  76 

63.91 

56.04 

63.66 

56.32 

63.41 

56  .  60 

85 

86 

64.90  !  56.42 

64.66 

56  .  70 

64.41 

56.99 

64.16 

57  .  27 

86 

87, 

65.66  57.08 

65.41 

57.36 

65.16 

57.65 

64.91 

57.93 

87 

88 

66.41 

57  .  73 

66.16 

58.02 

65.91 

58.31 

65.65 

58.60 

88 

89 

67.17 

58.39 

66.91 

58.68 

66.66 

58.97 

66.40 

59  .  26 

89 

90 

67.92 

59.05 

67.67 

59.34 

67.41 

59.64 

67.15 

59  .  93 

90 

91 

68.68 

59  .  70 

68.42 

60.001 

68.15 

60.30 

67.89 

60.60 

91 

92 

69.43 

60.36 

69.17 

6-0.66 

68.90 

60.96 

68.64 

61.26 

92 

93 

70.19 

61.01 

69.92 

61.32 

69.65 

61.62 

69.38 

61.93 

93 

94 

70.94 

61.67 

70.67 

61.98 

70.40 

62.29 

70.13 

62  .  59 

94 

95 

71.70 

62.33 

71.43 

62.64 

71.15 

62.95 

70.88 

63  .  26 

95 

96 

72.45 

62.98 

72.18 

63.30 

71.90 

63.61 

71.62 

63.92 

96 

97 

73.21 

63.64 

72.93 

63.96 

72.65 

64.27 

72.37 

64.59 

97 

98 

73.96 

64.29 

73.68 

64.62 

73.40 

64.94 

73  .  1  1 

65.26 

98 

99 

74.72 

64.95 

74.43 

65  .  28 

74.15 

65.60 

73.86 

6«j  .  92 

99 

100 

75.47 

65.61 

75.18 

65.93 

74.90 

66.26 

74.61 

66.59 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

g 

d 

03 

3 

49  Deg. 

48|  Deg. 

48£  Deg. 

48i  Deg. 

01 

P 

TBAVERSE    TABLE. 


K' 

42  Deg. 

42*  Deg. 

42£  Deg. 

42!  Deg. 

O 
55* 

p 

pT 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

1 

0.74 

0.67 

0.74 

0.67 

0.74 

0.68 

0.73 

0.68 

1 

2 

1.49 

1.34 

1.48 

1.34 

1.47 

1.35 

1.47 

1.36 

2 

3 

2.23 

2.01 

2.22 

2.02 

2.21 

2.03 

2.20 

2.04 

3 

4 

2.97 

2.68 

2.96 

2.69 

2.95 

2.70 

2.94 

2.72 

4 

5 

3.72 

3.35 

3.70 

3.36 

3.69 

3.38 

3.67 

3.39 

5 

6 

4.46 

4.01 

4.44 

4.03 

4.42 

4.05 

4.41 

4.07 

6 

7 

5.20 

4.68 

5.18 

4.71 

5.16 

4.73 

5.14 

4.75 

7 

8 

5.95 

5.35 

5.92 

5.38 

5.90 

5.40 

5.87 

5.43 

8 

9 

6.69 

6.02 

6.66 

6.05 

6.64 

6.08 

6.61 

6.11 

9 

10 

7.43 

6.69 

7.40 

6.72 

7.37 

6.76 

7.34 

6.79 

10 

11 

8.17 

7.36 

8.14 

7.40 

8.11 

7.43 

8.08 

7.47 

11 

12 

8.92 

8  .03 

8.88 

8.07 

8.85 

8.11 

8.81 

8.15 

12 

13 

9.66 

8.70 

9.62 

8.74 

9.58 

8.78 

9.J55 

8.82 

13 

14 

10.40 

9.37 

10.36 

9.41 

10.32 

9.46 

10.28 

9.50 

14 

15 

11.15 

10.04 

11.10 

10.09 

11.06 

10.13 

11.01 

10.18 

15 

16 

11.89 

10.71 

11.84 

10.76 

11.80 

10.81 

11.75 

10.86 

16 

17 

12.63 

11.38 

12.58 

11.43 

12.53 

11.48 

12.48 

11.54 

17 

18 

13.38 

12.04 

13.32 

12.10 

13.27 

12.16 

13.22 

12.22 

18 

19 

14.12 

12.71 

14.06 

12.77 

14.01 

12.84     13.95 

12.90 

19 

20 

14.86 

13.38 

14.80 

13.45 

14.75 

13.51     14.69 

13.58 

20 

21 

15.61 

14.05 

15.54 

14.12 

15".  48 

14.19 

15.42 

14.25 

21 

22 

16.35 

14.72 

16.28 

14.79 

16.22 

14.86 

16.16 

14.93 

22 

23 

17.09 

15.39 

17.02 

15.46 

16.96 

15.54 

16.89 

15.61 

23 

24 

17.84 

16.06 

17.77 

16.14 

17.69 

16.21 

17.62 

16.29 

24 

25 

18.58 

16.73 

18.51 

16.81 

18.43 

16.89 

18.36 

16.97 

25 

26 

19.32 

17.40 

19.25 

17.48 

19.17 

17.57 

19.09 

17.65 

26 

27 

20.06 

18.07 

19.99 

18.15 

19.91 

18.24 

19.83 

18.33 

27 

2S 

20.81 

18.74 

20.73 

18.83 

20.64 

18.92 

20.56 

19.01 

28 

29 

21.55 

19.40 

21.47 

19.50 

21.38 

19.59 

21.30 

19.69 

29 

30 

22.29 

20.07 

22.21 

20.17 

22.12 

20.27 

22.03 

20.36 

30 

31 

23  .  04 

20.74 

22.95 

20.84 

22.  86 

20.94 

22.76 

21.04 

31 

32 

23.78 

21.41 

23.69 

21.52 

23.59 

21.62 

23.50 

21.72 

32 

33 

24.52 

22.08 

24.43 

22.19 

24.33 

22.29 

24.23 

22.40 

33 

34 

25.27 

22.75 

25.17 

22.86 

25.07 

22.97 

24.97 

23.08 

34 

35 

26.01 

23.42 

25.91 

23.53 

25.80 

23.65 

25.70 

23  .  76 

35 

36 

26.75 

24.09 

26.65 

24.21 

26.54 

24.32 

26.44 

24.44 

36 

37 

27  50 

24.76 

27.39 

24.88 

27.28 

25.00 

27.17 

25.12 

37 

38 

28.24 

25.43 

28.13 

25.55 

28.02 

25.67 

27.90 

25.79 

38 

39 

28.98 

26.10 

28.87 

26.22 

28.75 

26.35 

28.64 

26.47 

39 

40 

29.731  26.77 

29.61 

26.  8'J 

29.49 

27.02 

29  .37 

27.15 

40 

41 

30.47 

27.43 

30.35 

27.57 

30  .  23 

27.70 

30.11 

27.83 

41 

42 

31.21 

28.10 

31.09 

28.24 

30.97 

28.37 

30.84 

28.51 

42 

43 

31.96 

28.77 

31.83 

28.91 

31.70 

29.05 

31.58 

29.19 

43 

44 

32.70 

29.44 

32.57 

29.58 

32.44 

29.73 

32.31 

29.87 

44 

45 

33.44 

30.11 

33.31 

30.26 

33.18 

30.40 

33.04 

30.55 

45 

46 

34.18 

30.78 

34.05 

30.93 

33.91 

31.08 

33.78 

31.22 

46 

47 

34.93 

31  .45 

34.79 

31.60 

34.65 

31.75 

34.51 

31.90 

47 

48 

35.67 

32.12 

35.53 

32.27 

35.39 

32.43 

35.25 

32.58 

48 

49 

36.41 

32.79 

36.27 

32.95 

36.13 

33.10 

35.98 

33.26 

49 

50 

37.16 

33.46 

37.01 

33.62 

36.86 

33.78 

36  .  72 

33.94 

50 

§ 
e 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

c 
a 

» 

1 

Sfl 

0 

48  Deg. 

47|  Deg. 

47i  Deg. 

474  Deg. 

S 

TRAVERSE    TABLE 


87 


0 

42  Deg. 

42i  Deg. 

42i  Deg. 

42|  Deg. 

O 

5T 
& 

1 

3 
o 
ft 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

51 

37.90    34.13 

37.75 

34.29 

37.60 

34.46 

37.45 

34.62 

51 

52 

38.64 

34.79 

38.49 

34.96 

38.34 

35.13 

38.18 

35.30 

52 

53 

39.39 

35.46 

39.23 

35.64 

39.08 

35.81 

38.92 

35.98 

53 

54 

40.13 

36.13 

39.97 

36.31 

39.81 

36.48 

39.65 

36.66 

54 

55 

40.87 

36.80 

40.71 

36.98 

40.55 

37.16 

40.39 

37.33 

55 

56 

41.62 

37.47 

41.45 

37.65 

41.29 

37.83 

41.12 

38.01 

56 

57 

42.36 

38.14 

42.19 

38  .  32 

42.02 

38.51 

41.86 

38.69 

57 

58 

43.10 

38.81 

42.93 

39.00 

42.76 

39.18 

42.59 

39.37 

58 

59 

43.85 

39.48 

43.67 

39.67 

43.50 

39.86 

43.32 

40.05 

59 

60 

44.59 

40.15 

44.41 

40.34 

44.24 

40.54 

44.06 

40.73 

60 

61 

45  .  33 

40.82 

45.15 

41.01 

44  .  97 

41.21 

44.79 

41.41 

61 

62 

46.07 

41.49 

45.89 

41.69 

45.71 

41.89 

45.53 

42.09 

62 

63 

46.82 

42.16 

46.63 

42  .  36 

46.45 

42.56 

46.26 

42.76 

63 

64 

47.56 

42.82 

47.37 

43.03 

47.19 

43.24 

47.00 

43.44 

64 

65 

48.30 

43.49 

48  .  1  1 

43  .  70 

47.92 

43.91 

47.73 

44.12 

65 

66 

49.05 

44.16 

48  .  85 

44.38 

48.66 

44.59 

48.47 

44.80 

66 

67 

49  .  79 

44:83 

49  .  59 

45.05 

49.40 

45.26 

49.20 

45.48 

67 

68 

50.53 

45  .  50 

50  .  33 

45  .  72 

50.13 

45.94 

49.93 

46.16 

68 

69 

51.28 

46.17 

51.07 

46  .  39 

50.87 

46.62 

50.67 

46.84 

69 

70 

52.02 

46  .  84 

51.82 

47.07 

51.61 

47.29 

51.40 

47.52 

70 

71 

52  .  76. 

47*5  1 

52  .  56 

47.74 

52.35 

47.97 

52.14 

48.19 

71 

72 

53.51 

48.18 

53.30 

18.41 

53  .  08 

48.64 

52.87 

48.87 

72 

73 

54.25 

48.85 

54.04 

49.08 

53.82 

49.22 

53.61 

49.55 

73 

71 

54.99 

49.52 

54.78 

19  .  76 

54.56 

49.99 

54.34 

50.23 

74 

75 

55  .  74 

50.18 

55.52 

50.43 

55.30 

50.67 

;55.07 

50.91 

75 

76 

56.48 

50.85 

56.26 

51.10 

56.03 

51.34 

55.81 

51.59 

76 

77 

57  .  22 

51.52 

57.00 

5  L  .  77 

56  .  77 

52.02 

56.54 

52.27 

77 

78 

57.97    52.19 

57.74 

52.44 

57.51 

52.70 

57.28 

52.95 

78 

79 

58.71  1  52.86 

58.48 

53.12 

58  .  24 

53.37 

58.01 

53.63 

79 

80 

59.45]  53.53 

59.22 

53  .  79 

58.98 

54.05 

58.75 

54.30 

80 

81 

60.19  !  54.20 

59  .  96 

54.46 

59  .  72 

54.72 

59.48 

54.98 

81 

82 

60.94    54.87 

60.70 

55.13 

60.46 

55.40 

60.21 

55.66 

82 

83 

61.68    55.54 

61.44 

55.81 

61.19 

56.07 

60.95 

56.34 

83 

84 

62  .  42 

56  .  2  1 

62.18 

56  .  48 

61.93 

56  .  75 

61.68 

57.02 

84 

85 

63  .  1  7 

56.  8  3 

62  .  92 

57.  15 

02.67 

57.43 

62.42 

57.70 

85 

86 

63.91     57.55 

63.66 

57.82 

63.41 

58.10 

63.15 

58.38 

86 

87 

64.651  58.21 

64.40 

53  .  50 

(54.14 

58  .  78 

63.89 

59.06 

87 

88 

65.40 

58.88 

65  .  1  4 

59.17 

64.88 

59.45 

64.62 

59.73 

88 

89 

66.14 

59.55 

65.88 

59.84 

65.62    60.13 

65.35 

60.41 

89 

90 

66.88 

60.22 

66.62 

60  .  ft  I 

66.35 

60.80 

66.09 

61.09 

90 

91 

67.63 

60.89 

67.36 

61.19 

67.09 

61.48 

66.82 

61.77 

91 

92 

68.37 

61.56 

63.10 

61.86 

67.83 

62.15 

67.56 

62.45 

92 

93 

69.11 

62  .  23 

68.84 

62  .  53 

68.57 

62.83 

68.29 

63.13 

93 

94 

69.86 

62.90 

69  .  53 

63.20 

69.30 

63.51 

69.03 

63.81 

94 

95 

70.60 

63.57 

70.32 

63  .  87 

70.04 

64.18 

69.76 

64.49 

95 

96 

71.34 

64.24 

71.06 

64.55 

70.78 

64.86 

70.49 

65.16 

96 

97 

72.08 

64.  9i 

71.80 

65.22 

71.52 

65.53 

71.23 

65.84 

97 

93 

72.83 

65.57 

72.54 

65.89 

72.25 

66.21 

71.96 

6(5.52 

OS 

99 

73.57 

66.24 

73.28 

66.56 

72.99 

66.88 

72.70 

67.20 

99 

100 

74.31 

66.91 

74.02 

67.24 

73.73 

67.56 

73.43 

67.88 

100 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<D 
O 

1 

3 

48  Deg. 

47|  Deg. 

47£  Deg. 

47*  Deg. 

1 

13* 


TRAVERSE    TABLE. 


s 

43  Deg. 

434  Deg. 

43i  Deg. 

43|  Deg. 

C 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I 

1 

0.73 

0.68 

0.73 

0.69  1 

0.73 

0.69  ! 

0.72 

0.69 

1 

2 

1.46 

1.36 

1.46 

1.37 

1.45 

1.38 

1.44 

1.38 

2 

3 

2.19 

2.05 

2.19 

2.06 

2.18 

2.07 

2.17 

2.07 

3 

4 

2.93 

2.73 

2.91 

2.74 

2.90 

2.75 

2.89 

2.77 

4 

5 

3.66 

3.41 

3.64 

3.43 

3.63 

3.44 

3.61 

3.46 

5 

6 

4.39 

4.09 

4.37 

4.11 

4.35 

4.13 

4.33 

4.15 

6 

7 

5.12 

4.77 

5.10 

4.80 

5.08 

4.82 

5.06 

4.84 

7 

8 

5.85 

5.46 

5.83 

5.48 

5.80 

5.51 

5.78 

5.53 

8 

9 

6.58 

6.14 

6.56 

6.17 

6.53 

6.20 

6.50 

6.22 

9 

10 

7.31 

6.82 

7.28 

6.85 

7.25 

6.88 

7.22 

6  92 

10 

11 

8.04 

7.50 

8.01 

7.54 

7.98 

7.57 

7.95 

7.61 

11 

12 

8.78 

8.18 

8.74 

8.22 

8.70 

8.26 

8.67 

8.30 

12 

13 

9.51 

8.87 

9.47 

8.91 

9.43 

8.95 

9.39 

8.99 

13 

14 

10.24 

9.55 

10.20 

9.59 

10.16 

9.64 

10.11 

9.68 

14 

15 

10.97 

10.23 

10.93 

10.28 

10.88 

10.33 

10.84 

10.37 

15 

16 

1  1  .  70 

10.91 

11.65 

10.96 

1  1  .61 

11.01 

11.56 

11.06 

16 

17 

12.43 

11.59 

12.38 

11.65 

12.33 

11.70 

12.28 

11.76 

17 

18 

13.16 

12.38 

13.11 

12.33 

13.06 

1:2.39 

13.00 

12.45 

18 

19 

13.90 

12.96 

13.84 

13.02 

13.78 

13.08 

13.72 

13.14 

19 

20 

14.63 

13.64 

14.57 

13.70 

14.51 

13.77 

14.45 

13.83 

20 

"21 

15.36 

14.32 

15.30 

14.39 

15.23 

14.46 

15^17 

14.52 

21 

22 

16.09 

15.00 

ID.  02 

15.07 

15.96 

15.14 

15.89 

15.21 

22 

23 

16.82 

15.69 

16.75 

15.76 

16.68 

15.83 

16.61 

15.90 

23 

24 

17.55 

16.37 

17.48 

16.44 

17.41 

16.52 

17.34 

1G.60     24 

25 

18.28 

17.05 

18.21 

17.13 

18.13 

17.21 

18.06 

17.29 

25 

26 

19.02 

17.73 

18.94 

17.81 

18.86 

17.90 

18.78 

1-7.98 

26 

27 

19.75 

18.41 

19.67 

18  50 

19.59 

18.59 

19.50 

18.67 

27 

28 

20.48 

19.10 

20.3* 

19.19 

20.31 

19.27 

20.23 

19.36. 

2P 

29 

21.21 

19.78 

21.12 

19.87 

21.04 

19.96 

20.95 

20.05 

29 

30 

21.94 

20.46 

21.85 

20.56 

21.76 

20.65 

21.67 

20.75 

30 

31 

22.67 

21.14 

22.58 

21.24 

22.49 

21.34 

22.39 

21.44 

31 

32 

23.40 

21.82 

23.31 

21.93 

23.21 

22.03 

23.12 

22.13 

32 

33 

24.13 

22.51 

24.04 

22.61 

23.94 

22.72 

23.84 

22.82 

33 

34 

24.87    23.19 

24.76 

23.30 

24.  «6    23.40 

24.56 

23.51 

34 

35 

25.60]  23.87 

25.49 

23.98 

25.39 

24.09 

25.28 

24.20 

gfx 

36 

26.33 

24.55 

26.22 

24.67 

26.11 

24.78 

26.01 

24  .  89 

36 

37 

27.06 

25.23 

26.95 

25.35 

26.84 

25.47 

26.73 

25.59 

37 

38 

27.79 

25.92 

27.68 

26.04 

27.56 

26.16 

27.45 

26.28 

38 

39 

28.52 

26.60 

28.41 

26.72 

28.29 

26.85 

28.17 

26.97 

39 

40 

29.25 

27.28 

29.13 

27.41 

29.01 

27.53 

28.89 

27.66 

40 

41 

29.99 

27.96 

29.86 

28.09 

29.74 

28.22 

29.  62 

28.35 

41 

42 

30.72 

28.64 

30.59 

28.78 

,30.47 

28.91 

30.34 

29.04 

42 

43 

31.45 

29.33 

31.32 

29.46 

31.19 

29.60 

31.06 

29.74 

43 

44 

32.18 

30.01 

32.05 

30.15 

31.92 

30.29 

31.78 

30.43 

44 

45 

32.91 

30.69 

32.78 

30  .  83 

32.64 

30.98 

32.51 

31.12 

45 

46 

33.64 

31.37 

33.51 

31.52 

33.87 

31.66 

33.23 

31.81 

46 

47 

34.37 

32.05 

34.23 

32.20 

34.09 

32.35 

33.95 

32.50 

47 

48 

35.10 

32.74 

34.96 

32.89 

34.82 

33.04 

34.67 

33.19 

48 

49 

35.84 

33.42 

35.69 

33.57 

35.54 

33.73 

35.40 

33.88 

49 

50 

36.57 

34.10 

36.42 

34.26 

36.27 

34.42 

36.12 

34.58 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

B 

O 

06 

I 

47  Deg. 

46|  Deg. 

46i  Deg. 

461  Deg' 

• 

3 

TRAVERSE    TABLE. 


g 

43  Deg. 

43*  Deg. 

43^  Deg. 

431  D«g. 

q 

1 

| 

3 
P 

Lat. 

Dep. 

Lat. 

Dop. 

Lat. 

Dep. 

Lat. 

Dep, 

51 

37.30 

34.78 

37.15 

34.94 

36.99 

35.11 

36.84 

35.27 

"51 

52 

38.03 

35.46 

37.88 

35.63 

37.72 

35.79 

37.56 

3o  .  96 

52 

53 

38.76 

36.15 

38.60 

36.31 

38.44 

36.48 

38.29 

36  .  65 

53 

54 

39.49 

36.83 

39.33 

37.00 

39.17 

37.17 

39.01 

37.34 

54 

55 

40.22 

37.51 

40.06 

37.69 

39.90 

37.86 

39  .  73 

38.03 

55 

56 

40.96 

38.19 

40.79 

38.37 

40.62 

38.55 

40.45 

38.72 

56 

57 

41.69 

38.87 

41.52 

39.06 

41.35 

39.24 

41.17 

39.42 

57 

58 

42.42 

39  .  56 

42.25 

39.74 

42.07 

39.92 

41.90 

40.11 

58 

59 

43.15 

40.24 

42.97 

40.43 

42.80 

40.61 

42.62 

40.80 

59 

60 

43.88 

40.92 

43.70 

41.11 

43.52 

41.30 

43.34 

41.49 

60 

61 

44.61 

41.60 

44.43 

41.80 

44.25 

41.99 

44.06 

42.18 

61 

62 

45.34 

42.28 

45.16 

42.48 

44.97 

42.68 

44.79 

42.87 

62 

63 

46.08 

42.97 

45.89 

43.17 

45.70 

43.37 

45.51 

43.57 

63 

64 

46.81 

43.65 

46.62 

43.85 

46.42 

44.05 

46.23 

44.26 

64 

65 

47.54 

44.33 

47.34 

44.54 

47.15 

44.74 

46.95 

44.95 

65 

66 

48.27 

45.01 

48.07 

45.22 

47.87 

45.43 

47.68 

45.64 

66 

67 

49.00 

45.69 

48.80 

45.91 

48.60 

46.1'* 

48.40 

46.33 

67 

68 

49  .  73 

46.38 

49.53 

46.59 

49.33 

46.81 

49.12 

47.02 

68 

69 

50.46 

47.06! 

50.26 

47.28 

50  .  05 

47.50 

49.84 

47.71 

69 

70 

51.19 

47.74 

50.99 

47.96 

50.78 

48.18 

50.57 

48.41 

70 

71 

51.93 

48.42 

51.71 

48.65 

51.50 

48.87 

51.29 

49.10 

71 

72 

52.66 

49.10 

52.44 

49.33 

52.23 

49  .  56 

52.01 

49.79 

72 

73 

53.39    49.79 

53.17 

50.02 

52.95 

50.25 

52  .  73 

50.48 

73 

74 

54.12 

50.47 

53.90 

50.70 

53.68 

50.94 

53.45 

51.17 

74 

75 

54.85 

51.15 

54.63 

51.39 

54.40 

51.63 

54.18 

51.86 

75 

76 

55.58 

51.83 

55.36 

52.07 

55.13 

52.31 

54.90 

52.55 

76 

77 

56.31 

52.51 

56.08 

52.76     55.85 

53.00 

55.62 

53  .  25 

77 

78 

57.05 

53.20 

56.81 

53.44 

56.58 

53.69 

56.34 

53.94 

78 

79 

57.78 

53.88 

57.54 

54.13 

57.30 

54.38 

57.07 

54.63 

79 

80 

58.51 

54.56 

58.27 

54.81 

58.03 

55.07 

57.79 

55.32 

80 

81 

59.24 

55.24 

59.00 

55.50 

58.76 

55  .  76 

58.51 

56.01 

81 

82 

59.97 

55.92 

59.73 

56.18 

59.48 

56.45 

59.23 

56.70|    82 

83 

60.70 

56.61 

60.45 

56.87 

60.21 

57.13 

59  .  96 

57.40 

83 

84 

61.43 

57.29 

61.18 

57.56 

60.93 

57.82 

60.68 

58.09 

84 

85 

62.17 

57  .  97 

61.91 

58.24 

6  1  .  66 

58.51 

61.40 

58  .  7S 

85 

88 

62.90 

58  .  65 

62.64 

58  .  93 

62.38 

59  .  20 

62.12 

59.47 

86 

87    63.63 

59.33 

63.37 

59.61 

63.11 

59.89 

62.85 

60.16 

87 

88 

64.36 

60.02 

84.10 

60.30 

63.83 

60.58 

63.57(60.85      88 

89 

65  .  09 

60  .  70 

64.82 

60.98 

64.56 

61.26 

64  .  29 

61.54      89 

90 

65.82 

61.38 

65.55 

61.67 

65.28 

61.95 

65.01 

62-24       90 

91 

66.55 

62.06 

66.28  162.35 

6ft.  01 

62.64 

65.74 

62.93      91 

92 

67.28 

62.74 

67.01 

63.04 

66  .  73 

63.33 

66.46 

63.62      92 

93 

68.02 

63.43 

67.74 

63  .  72 

67.46 

64.021  67.18 

64.31       93 

94 

68.75 

64.11 

68.47 

64.41 

68.19 

64.71 

67.90 

65.00       94 

69.48 

64.79 

69.20 

65.09 

68.91 

65  .  39 

68.62 

65.69 

95 

96    70.21 

65.47 

69.92 

65  .  78 

69.64 

66.08 

69.35 

66.39 

90 

97  '70.94 

66.15 

70.65 

66.46 

70.36 

66.77 

70.07 

67  .  08 

9? 

98 

71.67 

66.84 

71.37 

67.15 

71.09 

67.46 

70.79 

67.77 

98 

99 

72.40 

67.52 

72.11 

67.83 

71.81 

68.15 

71.51 

68.46 

99 

100 

73.14 

68.20 

72.84 

68.52 

72.54 

68.84 

72.24 

69.15 

100 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

8 

c 

1 
Q 

47  Deg. 

462  Deg. 

461  Deg. 

22 

P 

TRAVERSE    TABLE. 


jg 

44  Deg. 

44^  Deg. 

44£  Deg. 

44J  Deg. 

45  Deg. 

O 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

1 

0.72 

0.69 

0.72 

0.70 

0.71 

0.70 

0.71 

0.71 

0.71 

0.71 

1 

2 

1.44 

1.39 

1.43    1.40 

1.43 

1.40 

1.42 

1.41 

1.41 

1.41 

2 

3 

2.16 

2.08 

2.J5 

2.09 

2.14 

2.10 

2.13 

2.11 

2.12 

2.12 

3 

4 

2.88 

2.78 

2.87 

2.79 

2.85 

2.80 

2.84 

2.82 

2.83 

2.83 

4 

5 

3.60 

3.47 

3.58 

3.49 

3.57 

3.50 

3.55 

3.52 

3.54 

3.54 

5 

6 

4.32 

4.17 

4.30 

4.19 

4.28J  4.21 

4.26 

4.22 

4.24 

4.24 

6 

7 

5.04 

4.86 

5.01 

4.88 

4.99!  4.91 

4.97 

4.93 

4.95 

4.95 

7 

8 

5.75 

o.56 

5.73 

5.58 

5.71 

5.61 

5.68 

5.63 

5.66 

5.66 

8 

9 

6.47 

6.25 

6.45 

6.28 

6.42 

6.31 

6.39 

6.34 

6.36 

6.36 

9 

10 

7.19 

6.95 

7.16 

6.98 

7.13 

7.01 

7.10 

7.04 

7.07 

7.07 

10 

11 

7.91 

7.64 

7.88 

7.68 

7.85 

7.71 

7.81 

7.r/4 

7.78 

7.78 

11 

12 

8.63 

8.04 

8.PO 

8.37 

8.56 

8.41 

8.52 

8.45 

8.49 

8.49 

12 

13 

9.35 

9.03 

9.31 

9.07 

9.27 

9.11 

9.23 

9.15 

9.19 

9.19 

13 

14 

10.07 

9.73 

10.03 

9  .  77 

9.99 

9.81 

9.94 

9.86 

9.90 

9.90 

14 

15 

10.79 

10.42 

10.74 

10.47 

10.70 

10.51 

10.65 

10.56 

10.61 

10.61 

15 

16 

11.51 

11.11 

11.  46111.  16 

11.41 

11.21 

11.36 

ll.26ill.31 

11.31 

16 

17 

12.23 

11.81  |12.  18  11.86 

12.13 

11.92 

12.07 

11.971  12.02 

12.02 

17 

18 

12.95 

12.50 

12.89 

12.56 

12.84 

12.62 

12.78 

12.37  12.73 

12.73 

18 

19 

13.67  13.20 

13.61 

13.26 

13.55 

13.32 

13.49 

13.38  13.43 

13.43 

19 

20 

14.39  13.89 

14.33 

13.96 

14.26 

14.02 

14.20  14.  08114.14 

14.14 

20 

21 

15.11 

14.59  15.04 

14.65 

14.9SI14.72 

14.91  14.78114.85 

14.85 

21 

22  15.83 

15.28  15.76 

15.35 

15.69 

15.42 

15.62  15.49 

15.56 

15.56 

2-2 

23 

16.54 

15.  98  i!6.  47  16.05 

16.40 

16.12!  16.33 

16.19 

16.26 

16.26 

23 

24 

17.26 

16.67 

17.19ll6.75 

17.12 

16.82 

17.04 

16.90 

16.97 

16.97 

24 

25 

17.98 

17.37 

17.91 

17.44 

17.83 

17.52 

17.75 

17.60 

17.68 

17.68 

25 

26  118.70 

18.06 

18.62 

18.14 

18.54 

18.22 

18.46 

18.30 

18.38 

18.38 

26 

27 

19.42 

18.76  19.34 

18.84 

19.36 

18.92 

19.17 

19.01 

19.09 

19.09 

27 

28 

20.14 

19.45 

20.06 

:9.54 

19.97 

19.63 

119.89 

19.71 

19.80 

19.80 

28 

29 

20.86 

20.15 

20.77 

20.24 

20.68 

20.33|20.60 

20.42 

20.51 

20.51 

29 

3021.58 

20.84 

21.49 

20.93 

21.40 

21.03 

!21  .31 

21.12 

21.21 

21.21 

30 

31  22.30  21.53 

22.21 

21.63 

22.11 

21.73 

'22.02 

21.82 

21.92 

21.92 

31 

3223.02  22.23 

22.92 

22.33 

22.82 

22.43 

!22.  73 

22.  53  1|  22.  63 

22.63  3'2 

33  123.74  22.  92 

23.64 

23.03 

23.54 

23.13 

|23.44 

23.23 

23.33 

23.33J33 

34  124.4623.  62 

24.35 

23  .  72 

24  .  25 

23.83124.15 

23.94 

24.04 

24.04134 

35  25.  18124.31 

25  .  07 

24.42 

24.96 

24.53 

24.86 

24.64 

24.75 

24.7535 

36125.90  25.01 

25  .  79 

25.12 

25  .  68 

25.23 

25.57 

25.34 

25.46 

25.  46  i  36 

37  26.6225.70 

26  .  50 

25.82 

26.39 

25.93 

26.28 

26.05 

26.1626.163? 

38|27.33 

26.40 

27.22 

26.52 

27.  10 

26.63 

126.99 

26  .  75 

26.87 

26.87  38 

39128.05 

27.09 

27.94 

27.21 

27,82 

27.34 

'27.7027.46 

27.58 

27.58 

39 

40  28.  77  127.  79  1|28.  65 

27.91 

28  .  ii« 

28.04 

28.41 

28.16 

28.28 

28.28 

40 

41129.49 

28.481  29.  37128.  61 

29.24 

28.74 

29.12 

28.86 

28.99128.  99 

41 

42  20.21 

29.18  30.08J29,31 

29.96 

29.44 

29.83 

29.57 

20.7029.70 

42 

43 

30.93 

29.  87  130.  80 

30.00 

30.67 

30.14 

i30,54 

30.27 

30.41  30.41 

43 

44 

31.6530.56  31.52 

30  .  70 

31.38 

30.84 

:31.25 

30.98 

31.11  31.11 

44 

45 

32.37 

3  1  .  26 

32.23 

31.40 

32.10 

81.64l31.9631.6SJi31.82i31.83 

45 

46 

33.09 

3  1  .  95 

32.95 

32.10 

32.81 

32.24 

i32.  67132.  38||32.  53132.  53146 

47 

33.81 

32  .  65 

33.67 

32  .  80 

33  .  52 

32.94 

33.38 

33.  09  133.  23  33.  23  !4? 

48 

34.53 

33.34 

34.38 

33.49 

34.24 

33.64H34.09 

33.  79IJ33.  94!  33.  94  48 

49 

35  .  25 

34.04 

35.10 

34.19 

34.95 

34.34!!34.80 

34.50 

34.65:34.65 

49 

50 

35  .  97 

34.73 

35.82I34.89; 

35  .  66 

35.05  35.51 

35.20 

35.  36  135.  36 

50 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.    Lat. 

si 
o 

c 

3 

£ 

Q 

46  Deg 

45|  Deg. 

45^  Deg. 

45|  Deg. 

45  Deg. 

3 

TRAVERSE    TABLE. 


UH 

w 

&r 

i 
® 

"5! 

52 
53 
54 
55 
56 
57 
58 
59 
60 

44  Deg. 

44.}  Dcg. 

44i  Deg. 

44|  Deg. 

45  Deg. 

O 
% 

1 

Lat. 

Dep. 

35.43 

36.12 
36.82 
37.51 
38  .  2  1 
33.90 
39  .  60 
40.29 
40.98 
41.  6S 
42.37 
43.07 
43  .  76 
44.46 
45  .  i  5 
45  .  85 
46.  ni 
47.24 
47.93 
48  .  »i3 

Lat. 

Dep. 

Lat. 

Dep. 

35  .  75 
36.45 
37.15 
37.85 
38.55 
39  .  25 
39  .  95 
40.65 
41.35 
42.05 

Lat. 

36  .  22 
36.93 
37.64 
38.35 
39.06 
39.77 
40.48 
41.19 
41.90 
42.61 

Dep. 

Lai. 

Dcp. 

36  .  69 
37.41 
38.12 
38.84 
39.56 
40.28 
41.00 
41.72 
42.44 
43.16 
43.88 
44.80 
45.32 
46.04 
46.76 
47.48 
48.20 
48  .  92 
49.63 
50.35 
51.07 
51.79 
52.51 
53.23 
53.95 
54.67 
55.39 
56.11 
56.83 
57.55 

36.53 
37.25 
37.98 
38.68 
39.40 
40.11 
40  .  83 
41.55 
42.26 
42  .  98 

35  .  59 
36.29 
36.98 
37.68 
38  .  38 
39.08 
39.77 
40.47 
41.17 
41.87 

36.38 
37.09 
37.80 
38  .  52 
39  .  23 
39  .  91 
40.66 
41.37 
42.08 
42  .  79 
43~5l 
44  22 
44  93 
45.65 
46.36 
47.0? 
47.79 
48  .  50 
49.21 
49.93 

35.90  36.  OG 
36.61  36.77 
37.31  37.48 

38.  02;.38.  IS 
38.72!38.89 
39.42  39.60 
40.13  40.31 
40.83.i41.0l 
41.64rt41.72 
42.  24  !  142.43 

36.06 
36  .  77 
37.48 
38.18 
38.89 
39  .  60 
40  .  3  1 
41.01 
4  1  .  72 
42.43 

51 

52 
53 
54 
55 
56 
57 
58 
59 
GO 

61 
62 
63 
64 
65 
66 
67 
68 
69 
70 

43.69 
44.41 
45.13 

45.84 
46.56 
47.28 
47.99 
48,71 
49.42 
50.14 

42.57 
43.26 
43.96 
44.66 
45  .  36 
46.05 
46.75 
47.^5 
48.15 
48.85 

42.76 
43.46 
44.16 
44.86 
45.56 
46.26 
46.96 
47.66 
48.36 
49.06 

43.82 
44.03 
44.74 
45.45 
46.16 
46.87 
47.58 
48.29 
49.00 
49.71 

42.94; 
43.65! 
44.35: 
45.06 
45.76 
46.46! 
47.17 
47.87 
48.58 
49  .  28 

43.1343.13 

43.8443.84 
44.55144.55 
45.  25  !45.  25 
45.96,45.96 
46.67J46.67 
47.38j47.38 
48.08148.08 
48.7948.79 
49.50,49.50 

61 
62 
03 
(54 
65 
66 
67 
68 
69 
70 

71 

72 
73 
74 
75 
76 
77 
78 
79 
80 

49.  32  150.  86 
50.  02  151.57 
50.7l|!52.29 
51.40153.01 
52.10j53.72 
52.  7  9i  54.  44 
53.49':55.16 
54.18  55.87 
54.88  56.59 
55.57157.30 

49.54  50.64 
50.  24'  51.  35 
50.94152.07 
51.641152.78 
52.  33!  53.49 
53.03!  54.21 
53.73IJ  54.  92 
54.431  55.63 
55.13|  56.35 
55.82  57.06 

49.76 
50.47 
51.17 
51.87' 
52  .  57 
53.27 
53.97 
54.67 
55.37 
56  .  07 

50.42 
51.13 
51.84 
52.55 
53.26 
53.97 
54.68 
55.39 
56.10 
56.81 

49.98 
50.69 
51.39 
52.10 
52.80 
53.51 
54.21 
54.91 
55.62 
56.32 

50.  20;  50.  20 
50.91  50.91 
51.62  51.62 

52.3352.33 
53.0353.03 
53.7453.74 

54.4554.45 
55.1555.15 

55.  86  '55.  80 
56.57,56.57 

71 

72 
73 

74 
75 
76 

77 
78 
79 
80 

81 
82 
83 
84 
85 
86 
87 
88 
89 
90 

58.27 
58  .  99 
59.71 
60.42 
61.14 
61.86 
62.58 
63.30 
64.02 
64.74 
65.46 
66.18 
66.90 
67.62 
68.34 
69.06 
69.78 
70.50 
71.21 
71.93 

Dep. 

56  .  27 
56  .  96 
57.66 
58  .  35 
59  .  05 
59  .  74 
60.4-1 
61.13 
61.82 
62.52 

58.02 
:58.74 
'59.45 
60.17 
60.89 
61.60 
62  .  32 
163.03 
63.75 
64.47 

56.52 
57.22 
57.92 
58.61 
59.31 
60.01 
60.71 
61.41 
62.10 
62.80 

57  .  77 
58  .  49 
59.20 
59.91 
60.63 
61.34 
62.05 
62  .  77 
63.48 
64.19 

56.77 
57.47 
58.18 
58  .  88 
59  .  58 
60.28 
60.98 
61.68 
62.38 
63.08 

57.52 
58.24 
58.95 
59.66 
60.37 
61.08 
61.79 
62.50 
63.21 
63.92 

57.03 
57.73 
58.43 
59.14 
59.84 
60  .  55 
61.25 
61.95 
62.66 
63  .  36 

57.28  57.  23 
57.9857.98 
58.6958.69 
59.40  59.40 
60.1060.10 
60.81  60.81 
61.5261.52 
62.2362.23 
62.93  62.93 
63.6463.64 

HI 
82 
83 
84 
85 
86 
87 
88 
89 
90 

91 
92 
93 
94 
95 
96 
97 
98 
99 
100 

1 

5 
» 

63.2i    65.18 
63.91    65.00 
64.60-66.62 
65.30  67.33 
65.99168.05 
66.69J68.76 
67.38,69.  48 
68.08,70.20 
68.77i70.9l 
69.47!>:71.63 

63.50 
64.20 
64.89 
65  .  59 
66.29 
66.99 
67.69 
68.38 
69.08 
69.78 

64.91 
65.62 
66.33 
67.05 
67.76 
68  ,47 
69.19 
69.90 
70.61 
71.33 

63  .  7S 
64.48 
65.18 
65.89 
66  .  59 
67.29 
67.99 
68.69 
69.39 
70.09 

64.63 
65.34 
66.05 
66.76 
67.47 
68.18 
68.89 
69  .  60 
70.31 
71.02 

64.07 
64.77 
65.47 
66.18 
66.88 
67.59 
68.29 
68.99 
69.70 
70.40 

64.  3n  64.35 
65.05  65.0:') 
65.76  65.  7H 
66.47  66.47 
67.18167.18 
67.88<:67.88 
68.59168.59 
69.  30,69.30 
70.00  70,00 
70.71  70.71 

91 
92 
i   93 
94 
95 
96 
!   97 
i   98 
i   99 
ilOO 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 
45 

Lat.      8 

In 

Deg.     '  5 

46  Deg. 

45|  Deg. 

45     Deg. 

454  Deg.^ 

A   TABLE   OF  NATURAL   SIXES. 


0  De/. 

1  Deg. 

2  Deg. 

3  Deg. 

4  Deg. 

Nat.   N.  Co- 

Nat.  ;N.  Co- 

Nat. 

N.  Co- 

~N7At!  NTccT 

Nat.  N.  Co-" 

M 

Sine 

Sii.e 

Sine  1  Sine 

Sine 

Sine 

Sine 

Sine 

Sine 

Sine 

M 

0 

00000 

(Jnu. 

01745,99985 

03490 

99039 

05234 

99863 

06976 

99756 

60 

1 

00029  00000 

0177499984 

03519 

99938 

05263  99861 

07005 

99754 

59 

2  00058,100000 

01803  99984 

03548 

99937 

05292 

99860 

07034199752 

58 

2 

00087 

00000 

0183299983 

03577 

99936 

105321 

99858'  07063199750 

57 

4 

00116 

00000 

0186299983 

03606 

99935 

05350  99857  07092 

99748 

56 

5 

00145 

00000 

01891  99982 

03635 

99934 

05379  99855'  0712  J 

99746 

55 

6 

00175  00000 

01920199982 

03864 

99933 

05408 

99854 

07150 

99744 

54 

7 

0020400000 

01949 

99981 

03693 

99932 

05437 

99852  07179 

99742 

53 

8 
9 

0023300000 

00262(00000 

01978 
02007 

99980 
99980 

03723 
03752 

99931 
99930 

05466 

05495 

99851 
99849 

07208 
07237 

99740 
99738 

52 
51 

10 

00291100000 
00320J99999 

02036 
020G5 

99979 
99979 

03781 
03810 

99929 
99927 

05524 
05553 

99847 
99846 

07266 
07295 

99736 
99734 

50 

49 

12 

0034999999 

02094 

99978 

03839 

99926 

05582 

99844 

07324 

99731 

48 

13 

00378199999 

02123 

99977 

03868 

99925 

05611 

99842 

07353 

99729 

47 

14 

00407 

99999 

102152 

99977 

03897 

99924 

05640 

99841 

07382 

99727 

46 

15 

00436 

J19999 

02  1  8  1 

99976 

03926 

99923 

05669 

99839 

07411 

99725 

45 

16 

00465 

9999 

02211 

99976 

03955 

99922 

05698 

99838 

07440 

99723 

44 

IV 

00495 

99999 

02240 

99975 

03984 

99921 

05727 

99836 

07469 

99721 

43 

18 

00524 

99999  102269 

99974 

04013 

99919 

05756 

99834 

0749S 

99719 

42 

19 

00553  9999S 

02298 

99974! 

04042 

99918 

05785 

99833 

07527 

99716 

41 

20 

005821  99998 

0232? 

99973| 

04071 

99917 

05814 

99831 

0/556 

99714 

40 

21 

00611 

9999S 

02356 

(1997-7 

04100 

99916 

05844 

99829 

07585 

99712 

39 

22 

00640 

9999S 

02385 

999721 

04129 

99915 

05873 

99827 

07614 

99710 

38 

23 

00669 

99998 

02414 

99971J 

04159 

99913 

05902 

99826 

07643 

99708 

37 

24 

00698199998 

02443 

99970 

04188 

99912 

05931 

99824 

07672 

99705 

36 

25 
26 

00727 
007f-6 

99fi97 
99997 

02472  99969! 
02501  199969' 

04217 
04246 

J9911 
99910 

05960 
05989 

99822 
99821 

07701 
07730 

99703 
99701 

35 

34 

27 

00785  99J97 

02530 

99968' 

04275 

99909 

06018 

99819 

07754 

99699 

33 

28 
29 

00814:9999? 
00844199996 

02560 

02589 

99967:  04304 
99966  04333 

99907 
99906 

06047 
06076 

99817 
99815 

0778;- 
07817 

99696 
99694 

32 
31 

30 

00873  99996 

02618 

99966JJ04362 

99905 

06105 

99813 

07846 

99692 

30 

31  0090299996 
3200931  99996 

02647 
02676 

999651(04391 
099641104420 

99004 
99902 

06134 
06163 

99812 
99810 

07876 
07904 

99689 
99687 

29 

28 

33  00960  99995 

02705 

99963  04449 

99901 

06192 

99808- 

07933 

99685 

27 

34 

00989  99995 

02734 

99963  104478 

99900 

C6221 

99806 

07962 

99683 

26 

35 

OJOlif  99995 

02763 

99962 

0450? 

99898 

06250 

99804 

07991 

99680 

25 

36 

01017'99995 

92792 

99961  104536 

99897 

06279 

99803 

08020 

99678 

24 

37 

01076,99994 

02821 

99960 

04565 

09896 

06308 

99801 

0804!-) 

99676 

38 

01105199994 

02  450 

99959 

04594 

99894 

06337 

99799 

08078 

99673 

22 

39 

01134  99994 

028  79 

99959  04623 

99893 

06366 

99797 

08107 

99671 

21 

40 

01164  99993 

02908 

09958  '04653 

99892 

03395 

99795 

08136 

99668 

20 

41 

0119399993 

02938 

39957!  04682 

99890 

06424 

99793 

08165 

99666 

19 

42 

01222  99993 

02967 

99956:104711 

99889 

06453 

99792 

08194 

99664 

18 

43 

01251  99992 

02996 

99955J04740 

99888 

06482 

99790 

08223 

99661 

17 

44 

01280 

99992 

03025 

99954104769 

99886 

06511 

99788 

08252 

99659 

16 

45 

01309 

99991 

03054|  99953  04798 

99885 

06540 

99786 

08281 

99657 

15 

46 

01338199991 

03083 

19952  04827 

99883 

06569 

99784 

083  1  0 

99654 

14 

47 

01367 

99991 

13112 

99952  04856 

99882 

06598 

99782 

08339 

99652 

13 

48 

01396 

99990 

03141 

99951  04885 

99881 

06627 

997bO 

08368 

99649 

12 

49 

01425 

99990 

03170 

09950  04914  99879 

06656 

99778 

08397:99647 

11 

50 

01454 

99989 

03199 

99949  04943(99878 

06685 

99776 

08426  99644 

10 

51 

01483 

99989 

03228 

99948  04972  99876 

06714 

99774 

08455  99642 

9 

52 

01513 

99989 

03257 

99947:105001  99875  106743  '99772 

08484  99639 

8 

53 

01542 

99988 

03286 

99946  05030  99873 

06773,99770 

08513  99637 

7 

54 

01571 

99988 

03316  999451:0505999872 

06802(99768 

08542  99635 

6 

55 

01600 

99987 

)8345  99944  05088  99870 

06831 

99766 

08571  99632 

5 

56 

01629 

99987 

03374 

99943  0511799869 

06860 

99764 

08600  99630 

4 

5701658 

99986 

03403 

99942  05146 

99867)06889 

99762 

08629  99627 

3 

58101687 

9999^ 

13432 

90941  05175 

99S66JOS918  99760 

!)9625i  2 

59 

01716 

993S5 

>34fi  1 

39940  05205 

09S64J06947 

99753 

)8t587|99622|  1 

ft'  N.  Co- 

Nat 

,.  .  u- 

Nsit.  7v  '  ••>- 

"Nat.  ||N.  Co- 

>»'.. 

v  Co- 

Xat*  1  M 

Sine 

Sine 

si;ie   Sine  :!  Si'1".   Sine  jl  Sine 

Si  .ie  ||  Sine 

Sine 

'  fW  TW 

M  rw     ;«7  !i...r.     Hfi  i),..,   I  85  DP?. 

A   TABLE    OF    NATTTBAL    SINES 


93 


;  o  Deg. 

6  Deg. 

7  Dog. 

8  Deg. 

9  Deg. 

M 

N.  S. 

N.  CS. 

N.  S. 

N.CS. 

N.S. 

N.CS. 

N.S. 

N.CS. 

N.S. 

N.CS. 

M 

0 

08716 

99619 

10453 

9452 

12187 

99255 

13917 

99027 

15643 

98769 

30 

1 

08745 

99617 

10482 

9449 

12216 

99251 

13946 

99023 

15672198764 

^9 

2 

08774 

99614 

10511 

9446 

12245 

99248 

13975 

99019 

1570ll98760 

58 

3 

08803 

99612 

10540 

99443 

12274 

99244 

14004 

99015 

15730 

98755 

57 

4 

08831  '99609 

10569 

9440 

12302 

99240 

14033 

99011 

15758 

98751 

56 

5 

0886099607 

10597 

99437 

12331 

99237 

14061 

99006 

15787  98746 

55 

6 

08889  99604 

10626 

99434 

12360 

99233 

14090 

99002 

15816 

98741 

54 

7 

08918:99602 

10655 

99431 

12389 

99230 

14119 

98998 

15845 

98737 

53 

8 

08947  99599 

10684 

99428 

12418 

99226 

14148 

98994 

15873 

98732 

52 

9 

10 

08976  99596 
09005  99594 

10713 
10742 

99424 
99421 

12447 
12476 

99222 
99219 

14177198990 
14205  98986 

15902 
15931 

98728 
98723 

51 
50 

11 

09034 

99591 

10771 

99418 

12504 

99215 

14234 

98982 

15959 

98718 

49 

12 

09063 

99588 

10800 

99415 

12533 

99211 

14263 

98978 

15988 

9S714 

48 

13 

09092 

99586 

10829 

994-12 

12562 

99208 

14292 

98973 

16017 

98709 

47 

14 

09121  99533 

10858 

99409 

12591 

99204 

14320 

98969 

16046 

98704 

46 

15 

09150  99580 

10887 

99406 

12620 

99200 

14349 

98965 

16074 

98700 

45 

16 

09179 

99578  10916 

99402 

12649 

99197 

14378 

98961 

16103 

98695 

4-4 

17 

09208 

99575  10945 

99399 

12678 

991931  14407 

98957 

1G132 

98690 

43 

18 

09237!  99572 

10973 

99396 

12706 

99189 

14436 

98953 

16160 

98686 

42 

19 

09266  995^0 

11002 

99393 

12735 

99186 

14464 

98948 

16189  98681 

41 

20 

09295  99567 

11031 

99390 

12764 

99182 

14493 

98944 

I621b  CS676 

40 

21 

09324  99564 

11060 

99386 

12793 

99178 

14522  '98940 

16246 

98671 

39 

22 

09353199562 

11089 

99383 

12822 

99175 

14551 

98938 

16275 

98667 

38 

23J09382I99559 

11118 

99380 

12851 

99171 

14580 

98931 

16304 

98662 

37 

24 

09411  99556 

11147 

99377 

12880 

99167 

14608 

98927 

16333 

98657 

36 

25 
26 

09440199553 
09469  99551 

11176 
11205 

99374 
99370 

12908  99163 
12937)99160 

14637 
14666 

98923 
98919 

16361 
16390 

98652 
98648 

35 

34 

27 

09498 

99548 

1  1234 

99367 

12966 

99156 

14695 

98914 

16419 

98643 

33 

28 

09527 

99545  1  11263 

99364 

12995 

99152 

14723 

98910 

1  6447  i  98638 

32 

29 

09556  99542  Si  1291 

99360 

13024 

99148 

14752 

98906 

1  6476  1  98633 

31 

30 

095S5 

99540 

11320 

99357 

13053 

99144 

14781 

98902 

16505 

98629 

30 

31 

09614 

99537 

!  11349 

J9354 

13081 

99141 

'  148  10  98897 

16533 

98624 

29 

32 

09642 

99534 

'11378 

99351 

13110 

99137 

14838J98893 

16562 

98619 

28 

33 

09671 

99531  11407 

99347 

13139 

99133 

!l4867i98889 

16591 

98614 

27 

34 

09700 

99528J11436 

99344 

13168 

99129 

14896  98884 

16620 

98609 

26 

35 

09720 

995^6  11465 

99341 

13197 

99125 

14925  98880 

16648 

98604  25 

36 

09758 

995543  ;  11494 

J9337 

13226 

99122 

114954  98876 

1G677 

98600 

24 

37 

09787 

99520J  11523 

99334 

13254(99118 

11498298871 

I6706i  98595 

23 

38 

09816 

99517 

1  1  552 

99331 

13283  99114 

15011  198867 

16734  ',98590  1  22 

39 

09845 

99514 

'11580 

J9327 

13312  99110 

15040198863 

16763  98585)21 

40 

09874 

99511 

111609 

99324 

13341  99106 

15069 

98858 

16792  98580  20 

41 

09903 

99508 

:  11638 

J9320 

13370199102 

1509r, 

98854 

16820198575  19 

42 

0993i: 

99506 

1  11667 

99317 

13399  99098 

JJ5126 

98849 

16849  98570J18 

43 

09961 

99503!'  11696 

99314 

13427 

99094 

115155 

98845 

16878!  98565 

17 

44 

09990 

99500  11  11  725 

99310 

13456  99091 

115184  98841 

16906 

98561 

16 

45 

100L9 

99497 

111764 

99307 

!  3485]  99087 

1  152  12;  98836 

16935 

98556 

15 

4G 

10048 

094941  1  1783 

99303 

135H|990S3  H5241  '9*832 

•169G4I98551 

14 

47 

10077 

99491 

11812 

9080C 

13543 

990791  15270  9PS27 

16992  98546 

13 

48 

1040699488 

11840 

99297 

13572 

99075 

15292  9S823 

17021  98541 

12 

49 

1018699485 

111869 

99293 

13600 

99071 

!  15327  1988  18 

17050  98536 

11 

50 

10164994821  11898 

99290 

13629 

99067 

15356198814 

17078.98531 

10 

51 

10392  99479 

11927 

99286 

13658 

99063 

115385  98809 

17107  98526 

9 

52 

10221  '99476 

!  11956 

99283 

13687 

99059 

15414198805 

17136  98521 

8 

53 

10250  199473 

11985 

99279 

13716 

99055 

154  42  $8800 

17164  '98516 

7 

54 
55 
56 

10279 
10308 
10337 

99470 
99467 
99464 

J12014 
12043 
•12071 

99276 
99272 
99269 

13744 
13771] 
13802 

99051 
199047 
99043 

15471  J98796 
1550098791 

!;  15529  98787 

17193  98511 
1722298506 
17250:98501 

6 
5 

4 

57 

10366 

9946  1 

112100 

99265  ill  3831 

990391;  15557  198782 

17279  98496 

3 

58 

1039:' 

99458 

112129 

99262  !  13860  199035  111  5586  198778 

17308  98491 

2 

59 

10424(99455 

112158 

99258H1388C 

99031  1581E 

98773 

173:36  '98486 

1 

M 

N.CS.  N.  S. 

i  N.  eg. 

N.S.  .N.CS 

N.S. 

!  N.  CS 

N.S. 

N.  CS 

N.S. 

M 

M  Dry   1  ftf  Deg.   1  M  Deg. 

81  Deg. 

HO  Deg. 

94 


A    TABLE    OF    TXATUBAL    SINES. 


12  Deg. 

j   13  Deg.  1 

14  Deg. 

M 

N.S. 

N.  CS. 

:  N.S. 

N.  CS. 

N.S. 

N.  CS. 

|  N.  S.  1  N.  CS.  ! 

N.S. 

N.C8. 

M 

0 

17365 

98481 

19081 

98163 

20791 

97815 

22495 

97437  24192 

97030 

60 

1 

17393 

98476 

19109 

9815? 

20820 

97809 

[22623 

97430  24220  97023 

59 

2 

17422 

98471 

;19138 

98152 

20848 

97803 

i22552 

97424,24249  97015 

58 

3 

17451 

98466 

•19167 

98146 

20877 

97797 

22580 

974l7i|24277  97008 

57 

4 

17479 

98461 

!19195 

98140 

20905 

97791 

i22608 

97411  24305 

97001 

56 

5 

17508 

98455 

119224 

98135 

20933 

97784 

22637  197404!!24333  96994 

55 

6 

17537 

98450 

i!925" 

98129 

20962 

97778 

22665197398  24362  96987 

54 

7 

17565 

98445 

!1928l 

98124 

20990 

97772 

22693 

9739  11124390  96980 

53 

8 

17594 

98440 

119309 

98118 

21019 

97766 

22722 

97384  24418  96973 

52 

9 

17623 

98435 

119338 

98112 

21047 

97760 

22750 

97378: 

24446 

96966 

51 

10 

17651 

98430 

119366 

98107 

21076 

97754 

22778 

97371 

24474 

96959 

50 

11 

17680 

98425 

19395 

98101 

21104 

97748 

22807 

973651 

24503 

96952 

49 

12 

17708 

98420 

19423 

38096 

21132 

97742 

22835197358) 

24531 

96945 

48 

13 

14 

1773798414 
17766  98409 

19452 
19481 

98090 
98084 

21161 
21189 

97735 
97729 

22863  97351 

22892  97345: 

24559 

24587 

96937 
96930 

47 
46 

15 

17794 

98404 

19509 

98079 

21218 

97723 

:22920 

97.fi38  124615 

96923 

45 

16 

17823 

98399 

19538 

98073 

21246 

97717 

22948 

97331  124644196916 

44 

17 
18 

17852 
17880 

983&4 
98389 

19566 
19595 

98067 
98061 

21275 
21303 

97711 
97705 

22977 
23005 

97325 

97318 

24672  1  96909 
24700196902 

43 

42 

19 

17909 

98383 

19623 

98056 

21331 

97698 

23033 

973  li 

24728|96894 

41 

20 

1793V 

y8378 

19652 

98050 

21360 

97692 

23062 

97304 

24756  96887 

40 

21 

17966 

98373 

19680 

98044 

21388 

97686 

23090 

97298124784 

96880 

39 

22 
23 

17995 
18023 

98368 
98362 

19709 
19737 

98039 
98033 

21417 
21445 

97680 
97673 

23118  9729  IJI24813 
23146  972841124841 

96873 
96866 

38 
37 

24 

18052 

9S357 

19766 

98027 

21474 

97667 

,23175 

97278  24869 

96858 

36 

25 

18081 

98352 

19794 

98021 

21502 

97661 

23203 

97271  24897 

96851 

35 

26 

18109 

98347 

19823 

98016 

21530' 

97(555 

2323  1 

97264  24925 

96844 

34 

27 

18138 

98341 

19851 

98010 

21559 

97.648 

23260 

97967  84953 

96837 

33 

28 

18166 

98336 

19880 

98004 

21587 

97642 

23288 

97251  24982 

96829 

32 

29 
30 

18195 
18224 

98331 
98325 

19908 
19937 

97998 
9799-2 

21616 

21644 

97636 
97630 

23316  97244JJ25010 
23315  97237  J25038 

96822 
96815 

31 
30 

31 

18252 

98320 

19965 

97987 

2i672 

97623 

23373  97230  '25066196807 

29 

32 

18281 

98315 

19994 

97981 

21701 

97617 

2340  lj  97223 

25094  96800 

28 

33 

18309 

98310 

20022 

97975 

21729 

976  1  1 

23429  97217 

25122 

96793 

27 

34 

18338 

98304 

20051 

97969 

21758 

97604 

'2345897210 

25151 

96786 

26 

35 

18367 

98299 

20079 

97963 

21786 

97598 

23486197203 

25179 

96778 

25 

3ti 

18395 

98294  II  20  108 

97958 

21814 

97592 

12351497196 

25207 

96771 

24 

3? 

38 
39 
40 
41 

18424 
18452 
18481 
18509 

18538 

98288  ,20136 
98283:20165 
98277  20193 

98272  20222 
98267!  20250 

J7952 
97946 
97940 
97934 
97928 

21843 
2187] 
21899 
21928 
21956 

97585  123542(97189 

97579  23571  97182 
97573  12359997176 
97506  23627  97169 
97560  123656  971C2 

25235 
25263 
25291 
25320 
25348 

96764 
96756 
96749 
96742 
96734 

23 

22 
21 
20 
19 

42 
43 

18567 
18595 

98261 
98256 

20279 
120307 

97922121985 
97916  22013 

97553  123684  97155 
97547  P23712  97148 

25376 
25404 

96727 
96719 

18 
17 

44 

18624 

98250  i20336 

97910  22041  97541 

1237409714} 

25432 

96712 

16 

45 

18652 

98245  20-364 

97905 

22070 

97534 

123769197134 

25460 

96705 

15 

46 

18681 

98240  ;  20393 

97899  22098 

97528  j  23797  1  97  127 

25488 

96697 

14 

47 

18710 

98234 

20421 

97893 

22126 

97521 

23825197120 

25516 

96690 

13 

48 
49 

18738 
18767 

98229  20450 
98223  j  20478 

97887 
97881 

22155 

22183 

97515j23853|97113 

97508|:23882i97l06 

25545  96682 
25573J96675 

12 
11 

50 
51 
52 

18795 
18824 
18852 

98218  20507 
98212b0535 
98207  120563 

97875)22212 
97869  122240 
97863  22268 

97502  H23910 
974961:23938 
97489  123966 

97100 
97093 
97086 

25601(96667 
2562996660 
2565796653 

10 
9 

8 

53 

18881 

98201 

120592 

97857  J22297 

97483  |23995  97079 

2568596645 

7 

54 

18910 

98196 

20620 

97851  ;22325 

97476 

124023  97072 

25713196638 

6 

55 

18938 

98190 

(20649 

97845P22353  97470 

24051 

97085 

25741  96630 

5 

56 

18967 

98185 

120677 

97839  22382197463 

24079  97058 

25769  96623 

4 

57 

18995 

98179 

!20706 

97833  :j224rl  01  97457 

1241  08  197051 

25798:96615 

3 

58 

19024 

98174 

120734 

97S27  :  22438 

97450 

;24136 

97044 

25826,96608 

2 

59 

19052 

98168120763 

97821  224*57  97444 

24164 

97037 

25354  96600 

1 

M 

N.  CS.  N.  S.  1  N.  CS. 

N.S.   N.  <;.s.  N.S. 

j  N.  cs: 

N.S. 

N.  CS.  N.  S. 

M 

79  De£.     7«  Dear.   .  77  H.V.- 

76  l;cg 

75  \)vif. 

A    TABLE    OP    NATURAL    SINES. 


15  De/.   !   16  l>«tr. 

1?  JJeg. 

18  Ueg. 

19  Ueg. 

M 

M  N,».  N.  ori.  1 

N.  S.  N,  CS. 

N.  S, 

N,  CS. 

NTS 

N.CS. 

N.8. 

N  CS 

0  35882196593 

27564  96126 

29237 

95630 

30902 

95106 

32557 

94552 

60 

1  25910J985S5!  27592  96118 

29265 

95622 

30929 

95097 

32584 

94542 

59 

2  25933 

96578  127620  96  110 

29293 

95613 

30957 

95088 

32612 

94533 

58 

325968 

96570  1127648  96102 

29321  95605 

30985 

95079!|32639 

94523 

57 

4  25994 

96*S2  j  276  7696094 

29348195596 

31012 

95070,  32867 

94514 

56 

5126022 
6J26050 

96555!  27704 

96547127731 

98086 
96078 

29376  '95588 
29404  95579 

31040 
31068 

9506l! 
95052 

32894 
32722 

94504 
94495 

55 

54 

7i28feJ?9 

98540  {27759 

98070 

29432  95571 

31095 

95043 

32749 

94485 

53 

8J26107 

96532 

27787 

96062 

29460 

95562 

31123 

95033i  32777 

94476 

52 

926135 

96524 

27815' 

96054 

29487 

95554 

31151 

95024 

32304 

94466 

51 

10  26163 

988171 

-27843 

96046 

29515 

95545 

31178 

95015 

32832 

94457 

50 

Ilj28i91 

96509' 

27871 

96037 

29543,95536 

31206 

95006 

32859 

94447 

49 

1226219 

96502 

27899. 

96029 

29571195528 

31233  94997 

32887 

94438 

48 

13  26247 

96494 

27927; 

96021 

29599:95519 

31261194988 

32914 

94428 

47 

14:26275 

96486 

27955 

98013 

29628:95511 

31289  94979 

32942' 

94418 

46 

1526303 

96479 

27983 

98005 

29654 

95502 

31316 

94970 

32969 

94409 

45 

16  26331 

964  7  J 

280  1  1 

95997 

29682 

95493 

31344 

94961 

32997 

94399 

44 

1726359 

96483' 

28039 

959S9JJ29710 

95485 

31372 

94952 

33024 

94390 

43 

18  26387 

9'"*  456 

280.67 

95981  29737 

95476 

31399 

94943 

33051 

94380 

42 

19  23415 

9844? 

28095! 

95972 

29765 

95467 

31427 

94933 

33079 

94370 

41 

20126443 

964-10  J28  123 

95964 

29793 

95459 

31454 

94924 

3310H 

94361 

40 

21  12647  1,'964o3]j28  150 

95956 

29821 

95450 

H482 

94915 

33134 

94351 

39 

22  28:"iOi)  9642op28178 

95948 

29849 

95441 

31510 

94906 

33161 

94342 

38 

23  28528  984l7jj28206 

95940 

29S76 

95433 

31537 

94897 

33189 

94332 

37 

24  26556!  9H4  10 

28234 

.4593  I 

29904 

95424 

31565 

94888 

33216 

94322 

36 

25  26584 

96402 

28262 

.55923 

29932 

95415 

31593 

94878 

33244 

94313 

35 

26  26^12 

9*'  3  91 

28290 

35915 

29360 

95107 

31620 

94869 

33271 

94303 

34 

27  26840 

96386 

28318 

95907 

29987 

95398 

31648 

94860 

33298 

94293 

33 

281268H8 

96379 

28346 

95898 

30015 

95389 

31675 

94851 

33326 

94284 

32 

2926896  96371 

28374 

95890 

30043 

95380 

31703 

94842 

33353 

94274 

31 

30  26724J96383 

28402 

•J5882 

30071 

95372 

31730 

94832 

33381 

94264 

30 

31  26752 

96355 

23429 

95874 

30098 

95383 

31758 

94823 

33408 

94254 

29 

32:26780 

96347 

28457 

95865JJ30126 

95354 

31786 

94814 

33436 

94245 

28 

33  26808 

96340 

28485 

95857  30  154 

95345 

31813 

94805 

33463 

94235 

27 

34  26836 

96332ji28513 

95849  1130182 

9533,7 

31841 

94795 

33490 

94225 

26 

35!  26864 

96324  28541 

95841  30209 

9532* 

31868 

94786 

33518 

94215 

25 

36'26S92 

96316 

28569 

95832 

30237 

95319 

31896 

94777 

33545 

94206 

24 

37  126920 

96308 

28597 

95824 

30265 

95310 

31923 

94768 

33573 

94196 

23 

88126948 

96301 

28625 

95816 

30292 

35301 

31951 

94758 

33600 

94186 

22 

39(26976 

96293 

28652 

95807 

30320 

95293 

31979 

94749 

33627 

94176 

21 

40  j  27004 

96285 

28680 

95799 

30348 

95284 

32006 

94740 

33655 

94167 

20 

41  27032 

96277 

28708 

95791 

30376 

95275 

32034 

94730 

33682 

94157 

19 

42  27060 

96269 

28736 

95782 

30403 

95266 

32061 

94721 

33710 

94147 

18 

43  27088 

96261 

28764 

95774 

30431 

95257 

32089 

94712 

33737 

94137 

17 

4427H6 

96253 

28792 

95766 

30459 

95248 

32116 

94702 

33764 

94127 

16 

4527144 

96246 

28820 

95757 

30486 

95240 

32144 

94693 

33792 

94118 

15 

4627172 

96238 

28847 

95749 

30514 

95231 

32171 

94684 

33819 

94108 

14 

47  27200 

96230 

28875 

95740 

30542 

95222 

32199 

94674 

33846 

94098 

13 

48  27228 

98222 

28903 

95732 

30570 

95213 

32227 

94665 

33874 

94088 

12 

49  i  27256 

50,27284 

962  !  \ 
96206 

28959 

95724 
95715 

30597 
130625 

95204 
95195 

32254 

32282 

9465*5 
94646 

33901  94078 
33929  '94068 

11 
10 

51*27312 

96198 

28987  95707i|30653 

95186  32309 

94637 

33956!  94058 

9 

5227340 

96190 

29015  95698!  30680 

95177  32337  94627 

33983  94049 

8 

53:27368 

96182 

29042  95690J1  30708 

95168 

3236494618 

34011  94039 

7 

54,2739ft 

90171 

29070  95081 

30736 

95159 

32392  '94609 

34038  94029 

6 

55  '274-24 

96  160 

J29098  95673 

J30763 

9515()j|324l9l94599 

34065  94019 

5 

5627452 

96158 

29126195664 

'30791 

95142  32447 

94590 

34093  94009 

4 

57;  27480!  96  1  50 

129  154*95656 

130819 

95133  32474 

94580 

34120  93999 

3 

58'27r»i)8  !)^14~ 

j29I.*2  95647  ;30846.  95  124i!«32502 

94571 

14147  93989 

2 

59  <;7,S36  <)fi;3-! 

202°'}  |95639  ;!30874 

i95ll5!!32529 

94561 

•Hi  75  fi-3979 

1 

•»«  jN.«_-8  '•  N.S. 

r\.  cs.  N  s.  jj  N.  cs. 

N.  S.  i  N.  CS.  N.  S. 

\.  CS.  N.  S. 

JM 

74  Dear. 

73  Dejr.   |!   11  Dejr.   fl  71  Deg. 

~76~UeV~~ 

14 


A    TABLE    OF    NATURAL    SINES. 


20  Deg. 

;  21  Deg. 

22  Deg. 

23  Deg.  |   24  Deg. 

M 

N.S. 

N.CS. 

!  N.S. 

N.CS. 

N.S. 

N.CS. 

N.S. 

N.CS.   N.S. 

N.  CS. 

M 

0 

34202 

93969J  35837 

93358 

37461 

92718 

39073 

92050  J40674 

91355 

60 

1 

34229 

93959  '35864 

93348 

37488 

92707 

39100 

92039  40700 

91343 

59 

34257 

93949 

35891 

J3337 

37515 

92897 

39127 

92028140727  91331 

58 

3 

34284 

93939 

35918 

93327 

37542 

92686 

39153 

92016  40753  91319 

57 

4 

34311 

93929 

35945 

9331H 

37569 

92675 

39180 

92005  40780 

91307 

56 

5 

34339 

93919 

35973 

9330C  ;*7595 

92664 

39207 

91994  40806! 

91295 

55 

6 

34366 

93909 

36000 

93295 

37622 

92653 

39234 

91982  40833 

91283 

54 

7 

34393 

93899 

36027 

93285 

37649 

92642 

39260 

919711 

4086091272 

f>3 

8 

34421 

93889 

36054 

93274 

37676 

92631 

39287 

91959  40886|91260 

52 

9 

34448 

93879 

36081 

93264 

37703 

92620 

39314 

91948140913 

91248 

51 

10 

34475 

93869 

36108 

93253 

37730 

92609 

39341 

91936140939 

91236 

50 

11 

34503 

93859 

36135 

93243 

37757 

92598 

39367 

91925J40966 

91224 

49 

12 

34530 

93849 

36162 

93232 

37784 

92587 

39394 

91914  40992  91212 

48 

13 

34557 

93839 

36190 

93222 

37811 

92576 

39421 

91902  41019 

91200  47 

14 

34584 

93829 

36217 

93211 

37838 

92565 

39448 

91891!  41045191188  46 

15 

34612 

93819 

36244 

93201 

37865 

92554 

39474 

91879(41072 

91176 

45 

16 

34639 

93809  36271 

93190 

37892  92543 

39501 

91  868,  4~1  098 

91164 

44 

17 

34666 

93799  36298 

93180 

37919 

92532 

39528 

91856,41125  91152J43 

18 

34694 

93789 

36325 

93169 

37946 

92521 

39555 

91845|  41151 

91140142 

19 

34721193779 

36352 

93159 

37973 

92510 

39581 

91833 

41178 

91128141 

20 

34748  937  6C 

36379 

93148 

37999 

92499 

39608 

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1  60  Deg. 

98 


A   TABLE    OP    NATURAL   SINES. 


30  Deg. 

31  Deg. 

32  Deg. 

33  Deg. 

34  Deg. 

M 

N.S. 

N.CS. 

!  N.S. 

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N.CS. 

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M 

0 

50000 

86603 

51504 

85717 

52992 

84805 

54464 

83867 

55919 

82904 

60 

1 

50025 

86588 

51529 

85702 

53017 

84789 

154488 

83851 

55943  82887 

59 

2 

50050 

86573 

51554 

85687 

53041 

84774 

54513 

83835  55968  82871 

58 

3 

4 

50076 
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85672 
85657 

53066  j  84759  |54537 
53091184743  54561 

83819  55992  S2855 

83804  156016!  82839 

57 

56 

5 

50126 

86530  51628 

85642 

53115 

84728  54586 

83788  56040  82822 

55 

6 

50151(88515 

51653 

8562? 

53140 

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83772 

56064  82806 

54 

7 

50176 

86501 

51678 

85612 

53164 

84697 

54635 

83756 

56088  32790 

53 

8 
9 

50201 
50227 

86486 
86471 

51703 

51728 

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53189 
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84681 
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54659 
54683 

83740 

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5611282773 
56136  82757 

52 
51 

10 

50252 

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56  160;82741|  50 

11 

50277 

86442 

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84635 

54732 

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8272449 

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53288 

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54756 

83676; 

56208 

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13 

50327 

86413 

51828 

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53312 

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47 

14 

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56256 

82675 

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15 

50377 

86384 

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83629 

56280 

82659 

45 

16 

50403 

86369 

51902 

85476 

53386 

84557 

54854 

83613 

56:305 

82643 

44 

17 
18 
19 

50428 
50453 
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86354 
86340 
86325 

51927 
51  952 
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85431 

53411 
53435 
53460 

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43 

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41 

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53484  84495 
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40 
39 

22 

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38 

23 

50578  86266 

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55024 

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56473 

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37 

24 

50603 

86251 

52101 

85355 

53583 

84133 

55048 

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36 

25 

50628 

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52126 

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53607 

84417 

55072 

83469 

56521 

82495 

35 

26 

50654 

86222 

52151 

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53632 

84402 

55097 

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56545 

82478 

34 

27 

50679 

86207 

52175 

85310 

53656 

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55121 

83437 

56569 

82462 

33 

28 

50704  >  86  192 

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29 

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50829 

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33340 

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34 

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83324 

56736 

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23 

35 

50879 

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53853 

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55315 

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56760 

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25 

36 

50904 

86074  ,52399 

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53877 

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57 

58 

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8391  5  55847182953  1  57286  J8  1  965 
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3 
2 

59 

51479 

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83883  55895 

82920157334  81932 

J 

M 

N.  CS.  |  N.  S.  II  N.  OS. 

N.  S.  ;  N.  0<S. 

N.  S.  !  N.  CS. 

N.S.  llN.CS.  N.S. 

M 

59  Deg.   |  58  Deg.   ll  57  Pey.   |j  56  Deg.   ||  55  Deg. 

A    TABLE    OF    NATURAL   SINES. 


99 


35  Deg.  ||  36  Deg. 

37  L>eg. 

3«  Ueg. 

39  L>eg. 

M 

N.S. 

N.CS.  |j  N.S. 

N.  CS. 

N.sr 

N.CS. 

N.S. 

N.  CS. 

N.S. 

N.CS. 

M 

0 

57358 

81915158779  80902 

60182 

79864 

61566  78801 

62932 

77715 

60 

1 
2 

57381 
57405 

81  899  j  58802 
81882'  58826 

80885 
80867 

60205 

6022S 

79840 
79829 

61589 
61612 

7S783 
78765 

62955 
62977 

77696 
77678 

59 

58 

3 

57429 

81865 

58849 

80850 

60251 

7t'811 

61635 

78747  63000 

77660 

57 

4  57453 

5|57t77 

81848 
81832 

58873 
58896 

80833 
80816 

60274  79793 
60298  79776 

91658 
61681 

78729163022 
78711  63045 

77641 
77623 

56 
55 

6 

57501 

81815 

58920 

80799 

60321 

79758 

61704 

78694 

63068 

77605 

54 

7 

57524 

8  1  798  |58943 

80782 

60344 

79741 

61726 

78676 

63090 

77586 

53 

8  57548 

81782  J58967 

80765 

60367 

79723 

61749 

78658 

63113 

77568 

52 

9)57572 

81765 

158990 

80748 

60390 

79700 

61772 

78640 

63135 

77550 

51 

10 

57596 

81748 

59014 

80730 

60414 

79688 

61795 

78622 

63158 

77531 

50 

11 

57619 

81731 

59037 

80713 

60137 

79671 

61818 

78604 

63180 

77513 

49 

12 

57643 

81714 

5906  I 

80G96 

60460 

79053 

01811 

78586 

63203 

77494 

48 

13 

57667  81698 

59034 

80879 

69483 

79035 

61864 

78568 

63225 

77470 

47 

14 

57691 

81681 

59108 

80662 

60506 

79018 

61887 

78550 

63248 

77458 

46 

15 

57715 

81664 

59131 

80644 

60529  79600 

61909 

78532 

63271 

77439 

45 

16 

57738 

81647 

59154 

80627 

60553  795S3 

61932 

.78514 

63293 

77421 

44 

1  7!  57702 

81631 

59178 

S0610  60  57  0|  79565 

61955 

78493 

63316 

77402 

43 

i  s  '07736  SIGH 

59201 

80593 

60599]  79547 

61978 

78478 

63338 

77384 

42 

19157310  81597 

59225 

S0576 

60622)79530 

62001 

78460 

63361 

77366 

41 

20  1  57833  8  1580 

5  9248 

80558! 

60645  79512 

62024 

78442 

63383 

77347 

40 

21|57857,'81563 
22  57881  181546 
23  57901  81530 

59272 
59295 
59318 

80541 
80524 
3  9  507  i 

0;>(>63{  79494 
60691  79477 
6071479459 

62046 
62069 
62092 

78424 
78405 

78387 

63406 

63428 
63451 

77329 
77310 
77292 

39 
38 
?7 

24 

5792881513 

59342 

S0489! 

60738 

79441 

62115 

78369 

63473 

77273 

36 

2,"> 

5795281496 

59365 

S0472 

60761 

79424 

02138 

78351 

63496 

77255 

35 

26 

57976  81479 

59389 

80455 

60784 

79406 

62160 

78333 

63518 

77236 

34 

27 

57999 

814-62 

59412 

80438,60807 

793SS 

52183 

78315 

63540 

77218 

33 

28 

5802381445 

59436 

80420 

60830 

79371 

02206!  7S297  63563 

77199 

32 

29  58047  8  1428JI  59459 

80403 

60853 

79353 

62229 

78279!  63585 

77181 

31 

30  58070 

81412 

59482 

SO  386': 

'30870  79235 

32251 

78261  63608 

77162 

30 

31158094 

81395 

59505 

803681 

6089979318 

02274 

78243 

03630 

77144 

29 

32'53113  81378 

59529 

$03511100922  79300!  02297 

78225 

53653 

77125 

28 

3358141  813fil 

69552 

80334p60945l792c2||62320 

78206 

J3676 

77107 

27 

34 

58165  81344 

59576 

8031  6  |60968 

.79264162342 

78188 

013698 

77088 

26 

35 

58  1  89  LSI  327 

59599 

80299  16099  1 

79217102305 

78170 

33720 

77070 

25 

36  5S21  2  181310 

59622  80282  !|6  1015 

79229  j  62388 

78152 

03742 

77051 

24 

3?  58238  81203 

59646 

80264-1:61038 

7921  I  j  624  11 

73134 

03765 

77033 

23 

38:58200  81276 

59669 

80247  61  OG1 

791931 

62433 

781  16 

63787 

77014 

22 

39:58283  S1259 

59893  S0230  61084 

79176! 

62456 

78098 

63810 

76996 

21 

40  58307)  SI  242 

59716 

80212!  61  107 

79158; 

62479 

78079 

83332 

76977 

20 

41;f>S330j.81225 

59739 

80195;  61  139 

79140! 

62502 

78061 

03S54 

76959 

19 

•!2'583.j4|3J208  59763 
43:5837881191  i59786 

80l78i!6ll53j79122' 
801601  6  11  761  79  1051 

62524 
62547 

78043 
78025 

63877 
03899 

76940 
76921 

18 

17 

41  58401  81174 

.59809 

80143  61193  79087 

62670 

78007 

•J3922 

76903 

16 

45  58425 

81157159832 

SO  125|  6  12*22 

79069 

62592 

77988 

63944 

76884 

15 

40,58449  81  I40J'5'J«58i80l08i  01245 

7905  1 

62615 

77970 

63966 

76866 

14 

47158472  81  1  ^3jl59:.i7!J:^009  1  j!6  1208 

79033 

62638 

77952 

63989 

76847 

13 

48J58496  81106  50002  80073! 
49  58519  81039:  59020  89056i 

61291 
61314 

79015 
78998 

62660 
62683 

77934 
77916 

64011 
64033 

76828 
76810 

12 
11 

50  5S543  81072  59943  80038  61337 

78980 

62706 

77897 

T4056  78791 

10 

51  '53567  8l055j!59972  8002  ,61360 
52  53590;3103Sh5y995  SOOQ3;J61383 
53:58614jSl02l  »i>0i9  79986,;61406 

78962 
78944 
78  926  ! 

62728  77879!  H107S  73772 
62751  '.7780  1  >  »-i  100  70754 
62774  77843  ,Ul:i3  76735 

9 

8 
7 

5  1  586371  8  1  004 
55  58661  80987 

160042:79968  61429 
50065  7995  1  161451 

78908 
78891 

62796  ;  77824 
62819177806 

0414576717 
|64107  70098 

6 
5 

56i58684l80970  50089  '79934  j  6  1474  78873 

62842  77788 

64190  76679  4 

57:58708 

80953 

SD118  79916  6149T78856 

82864  77769  '.642  12  7606l!  3 

58  5873  1 

80936 

60135  79899  61520 

78837 

62S87  77751 

I64234l76642|  2 

5958755 

80919 

SO  158  7988  i:  01543 

78819 

02909  77733 

61256  76623 

1 

A! 

\.  *  t>.  N.  S. 

N.  CS.  i  N.  S.  !  N.  CS. 

N.  S. 

N.  CS. 

N.S. 

N.  CS. 

N.S. 

M 

j  54  Dei?,  ii  53  Deg.   \\  52  De?. 

51  D.-LT. 

1  50  Deg, 

fOO 


A   TABLE   OF   NATURAE 


M 

40  J 

N.S. 

~ff-cs. 

41  Deg.  1]  42  Ueg. 

43  Deg. 

44  Deg. 

M 

N.S. 

:N.CB,  N..S. 

N.CS. 

N.S. 

N.CS.. 

N.S. 

N.  CS. 

0 

64279 

76604 

65606 

7547  11669  13 

74314 

68200 

73135 

69466 

71934 

00 

1 
2 
3 

64301 
64323 
64346 

76586 
76567 
76548 

65628 
65650 
65672 

75452 
75433 
75414 

66935 
66956 
66978 

74295 
74276 
74256 

68221 
68242 
68264 

73116 
73096 
73076 

69487  71914 
69508  71894 
6952917187=3 

59 

58 
57 

4 

64368 

76530 

65894 

75395 

66999 

74237 

68285 

73056 

69549 

71853 

50 

5 

64390 

7651  1 

65716 

75375 

67021 

74217 

68306 

73036 

89570 

7183^ 

55 

6 

64412 

76492 

65738 

75356  67043 

74198  :  68327 

73016 

69591 

71813 

54 

!  7 

64435 

76473 

65759 

75337  67064 

74178 

68349 

72996 

69612171792 

,  8 

64457 

76455 

65781 

75318167086 

74159 

68370 

72976 

09633171772 

52 

9 

64479 

76436 

65803 

75299 

67107 

74139!  6839  1 

72957 

69654 

71752 

5i 

10 

64501  76417 

65825 

75280 

87129 

74120  68412 

72937 

89075 

71732 

f)0 

I 

64524 

76398 

65847  75261 

67151 

74100  08433 

72917 

69096 

71711 

4') 

12 

64546 

76380 

65869  75241 

87172 

74080  168455 

72897 

69717 

71691 

48 

13 
14 

04568  76381  i 
64590  76342 

65891 
65913 

75222  67194 
7520316-7215 

74051  ;68476 
74041  '68497 

72877  69737171671 
72857|(Jf  758171  650 

47 
40 

15  64512  76323 

65935 

75184J  67237 

74022  i:68M8 

72837  t  09779 

71030  45 

16 

64635 

76304 

65956 

75165  67258 

74002  6W539 

72817 

69800 

71610 

44 

17 

64657 

76286 

6597S 

75146167280 

73983 

68561 

72797  |V;9821 

71590 

43 

8 

64C79  76267 

66000 

751261  6730] 

73963 

68582 

72777  6  5)842 

71569 

42 

19 
20 

64701 
64723 

70248 
76229 

06022 
06044 

75  1071  67323 
750881  67344 

73944 
73924 

68803 
68624 

72757 
72737 

09862 
69883 

71549 
71529 

41 
40 

21 

64746 

76210 

60066 

75069! 

67366 

73904 

68645 

72717 

09904 

71508 

39 

1 

24 
25 
26 

64768 
64790 
64812 
64834 
64856 

76192 
761  ?3- 
76154 
76135 
76116 

60088 
66109 
06131 
00153 
66-1  75 

7505&1 
75030 

75011 
74992 
74-973! 

67387i  73885 
6740973865 
67430173846 
67452  73826 
G7473I73306' 

68666 

08088 
68709 
68730 
68751 

72697 
72677 
72657 
72637 
726  1  7 

09925  71488 
69946  71468 
099f  6  71-447 
69987)71427 
70008  71407 

38 
37 
36 
35 
34 

27 

64878 

76097 

09197 

74953" 

67495  73787  i:68772  72597 

70029 

713S6  33 

28 

64901 

78078 

06218 

74934 

67510  737071  68793J72577 

70049 

71366 

32 

29 

64923 

76059 

66240 

74915| 

67538  73747  16881  4^2557 

70070 

7  !  34o 

11 

30 

64945 

76041  [{66262 

74890 

07559 

737281 

688S&!  72537 

70091 

71325 

30 

31 

64967 

76022  j,66284 

74876 

07580 

737081 

680577*517 

701  12171305 

29 

32 

64989 

760031;  66306 

74857 

07002 

738881 

63878  i  72497 

70132  71284 

28 

33 

65011 

75984Ji$BSt7 

74  838 

07023 

73069! 

68899:72477 

70153 

71264 

27 

34 

650331  75965!:66349 

74818 

67645 

73649 

68920  72457 

70174 

71243 

26 

35 

65055 

75946  ,60871 

74799 

07608 

73029 

08  ;M  1,72437 

70  195 

71223 

25 

36 

65077  75927  60393 

74750 

07688 

73010 

08902  72417 

702  !  5 

7120:} 

24 

37 

65099  75908  .66414 

74760 

07709  735901 

689N3  72397 

7f)236 

71182 

23 

38 

65122 

75889166430 

74741 

'07736  !  75*570! 

0  900  172377 

70X57 

7  !  1  62 

22 

39 

05144 

75870 

66458 

74722 

J7752'|Vd551  ' 

09i:2">  72357 

70277 

71141 

21 

40 

05166 

7585  1 

664  SO 

74703 

67773  7:?53  1  1  [0901  R  72337 

7029  S 

711*21 

20 

41 

65188 

75832  66501 

74083 

677#ji733l  I  |69067J72317  70319 

71100 

19 

42 

65210 

758l3;.6ff522 

74004 

078Ifv73491jf09088  72297 

70339:71680 

18 

43 

65232 

75734 

:06f)15 

74644 

07837173472' 

09109:72277 

70-JB0171059 

17 

44 

65254 

75775  :6Gfj66 

74025 

07859  73^52 

09  130j  72257 

7038  1 

71039 

10 

45 

65270 

7jj75<>j66r588 

74006 

67880 

73432 

09  151  172236 

70401 

71019 

15 

40  05298 

75738  OG'olO 

745RO 

67901  [734  12 

091  72;  72216 

70422 

70998 

14 

47  65320 

75719  00032 

74507 

0792373393 

69193172196 

70443 

170978 

Id 

48i  65342J  75699  00653 

74548 

07944i73373 

69214172176 

70463 

;  70957 

12 

49 

65364  75080  66075'7452£ 

(37965 

73353 

'•9235  72150 

70484 

70937 

11 

50 

65386  175001  [66697 

74509 

67987 

73333 

69250  72130 

70505170916 

10 

51 
62 

65408J75642  66718 
65430  756231:  6674C 

74489 
74470 

6800S  73314 
08029  73294 

6927772116 

09298  72095 

70525 

70540 

70896 

70875 

9 

8 

53 

65452!75604  !6fi76S 

74451 

68051  73274 

0931972075 

70567 

70855 

i 

54 

65474  75585  6(578" 

74431 

68072173254 

53340172055 

70587  70834 

0 

55 

65490  755661  6680£ 

74412 

!  68093*  73234 

60361  72035 

70008 

70813 

f> 

56 

65518!75547|,C>8S27 

74392 

681  li 

>  73215 

I09i382f720lr, 

70628 

70793 

4 

57 

&5540  75528:  66S4& 

71373  68130  73195 

69403  71fJ95|J706<l?>  70772 

'A 

58 
58 
60 

65562;  75509.  06»7(. 
65584175490  6089  ' 
65606'  75471|  06911 

74353 
74334 
J  74314 

i  08  157  173  175 
68179-73155 
R820U73135 

69424  17  1  974  70670  70752 
69445  71  954J|?069(>,  707.; 
69466  7  1  934  i  707  11  70711 

'2 
\ 
(J 

M 

IToa 

N.  s.  |N.  rs 

N.S. 

N.  ('*?.  t  N.  8. 

N.  CS. 

N.S.  jjN.cs 

N.S 

M 

49  Deer.  ,    48  l^esr-   1  47  De«r. 

46  Dep.  ll  45  Deg. 

TABLE  OF  NATURAL  TANGENTS. 


101 


0  Degrees.     1  Degree. 

2  Degrees. 

3  Degrees. 

M 

N.Tan.,  N.  Cot.  .N.Tan.   N.  Cot. 

N.Tan.   N.  Cot. 

N.Tan 

N.  Cot. 

M 

0 

00000 

0000-00  01746 

57-2900 

03492  28-6363 

05241 

19-0811 

60 

1 

00029 

3437-75 

01775 

56-3506 

03521 

28-3994 

05270 

18-9755 

59 

2 

00058 

1718-87 

01804 

55-4415 

03550 

28-1664 

05299 

18-8711 

58 

3 

00087 

1145-92 

01833 

54-5613 

03579 

27-9372 

05328 

18-7678 

57 

4 

00116 

859-436 

01862 

53-7086 

03609 

27-7117 

05357 

18-6656 

56 

5 

00145 

687-549 

01891 

52-8821 

03638 

27-4899 

05387 

18-5645 

55 

6 

00175 

572-957, 

01920 

52-0807 

03667 

27-2715 

05416 

18-4645 

54 

7 

00204 

491-106 

01949 

51-3032 

03696 

27-0566 

05445 

18-3655 

53 

8 

00233 

429-718 

01978 

50-5485 

03725 

26-8450 

05474 

18-2677 

52 

9 

00262 

381-971' 

02007 

49-8157 

03754 

26-6367 

05503 

18-1708  51 

10 

00291 

343-7741 

02036 

49-1039 

03783 

26-4316 

05533 

18-0750 

50 

11 

00320 

312-521 

02066 

48-4121 

03812 

26-2296 

05562 

17-9801 

49 

12 

00349 

286-478 

02095 

47-7395 

03842 

26-0307 

05591 

17-8863 

48 

13 

00378 

264-441 

02124 

47-0853 

03871 

25-8348 

05620 

17-7934 

47 

14 

00407 

245-552 

02153 

46-4489 

03900 

25-6418 

05649 

17-7015 

46 

15 

00436 

229-182  02182 

45-8294 

03929 

25-4517 

05678 

17-6106 

45 

16 

00465 

214-858 

02211 

45-2261 

03958 

25-2644 

05708 

17-5205 

44 

17 

00495 

202-219 

02240 

44-6386 

03987 

25-0798 

05737 

17-4314 

43 

18 

00524 

190-984; 

02269 

44-0661 

04016 

24-8978 

05766 

17-3432 

42 

19 

00553 

180-932 

02298 

43-5081 

04046 

24-7185 

05795 

17-2558 

41 

20 

00582 

171-885 

02328 

42-9641 

04075 

24-5418 

05824 

17-1693 

40 

21 

00611 

163-700 

02357 

42-4335 

04104 

24-3675 

05854 

17-0837  39 

22 

00640 

156-259 

02386 

41-9158 

04133 

24-1957 

05883 

16-9990  38 

23 

00669 

149-465 

02415 

41-4106 

04162 

24-0263 

05912 

16-9150  37 

24 

00698 

143-237 

02444 

40-9174 

04191 

23-8593 

05941 

16-8319  36 

25 

00727 

137-507 

02473 

40-4358 

04220 

23-6945 

05970 

16-7496135 

26 

00756 

132-219 

02502 

39-9655 

04250 

23-5321 

05999 

16-6681 

34 

27 

00785 

127-321 

02531 

39-5059 

04279 

23-3718 

06029 

16-5874 

33 

28 

00814 

122-774 

02560 

39-0568 

04308 

23-2137 

06058 

16-507532 

29 

00&44 

118-540 

02589 

38-6177 

04337 

23-0577 

06087 

16-4283 

31 

30 

00873 

114-589 

02619 

38-1885 

04366 

22-9037 

06116 

16-3499i30 

~3~1 

00902 

110-892 

02648 

37-7686 

04395 

22-7518 

06145 

16-2722|  29 

32 

00931 

107-426 

02677 

37-3579 

04424 

22-6020 

06175 

16-1952,28 

33 

00960 

104-171 

02706 

36-9560 

04454 

22-4541 

06204 

16-119027 

34 

00989 

101-107 

02735 

36-5627 

04483 

22-3081 

06233 

16-0435  26 

35 

01018 

98-2179 

02764 

36-1776 

04512 

22-1640 

06262 

15-9687 

25 

36 

01047 

95-4895 

02793 

35-8006 

04541 

22-0217 

06291 

15-8945 

24 

37 

01076 

92-9085 

02822 

35-4313 

04570 

21-8813 

06321 

15-8211 

23 

38 

01105 

90-4633 

02851 

35-0695 

04599 

21-7426 

06350 

15-7483 

22 

39 

01135 

88-1436 

02S81 

34-7151 

04628 

21-6056 

06379 

15-6762 

21 

40 

01164 

85-9398 

02910 

34-3678 

04658 

21-4704 

06408 

15-6043 

20 

41 

01193 

83-8435 

02939 

JM'd&ttJI  04687 

21-3369 

06437 

15-5340  19 

42 

01222 

81-84^0 

02968 

33-6935 

04716 

21-2049 

06467 

15-4638 

18 

43 

01251 

79-9434 

02997 

33-3662 

04745 

21-0747 

06496 

15-3943 

17 

44 

01280 

78-1263 

03026 

33-0452 

04774 

20-9460 

06525 

15-3254 

16 

45 

0130& 

76-3900 

03055 

32-7303 

04803 

20-8188 

06554 

15-2571 

15 

46 

~6l338 

74-7292 

03084 

32-4213 

04832 

20-6932 

06584 

15-1893 

iT 

47 

01367 

73-1390 

03114 

32-1181 

04862 

20-5691 

06613 

15-1222 

13 

48 

01396 

71-6151 

03143 

31-8205 

04891 

20-4465 

06642 

15-0557 

12 

49 

01425 

70-1533 

03172 

31-5284 

04920 

20-3253 

06671 

14-9898 

11 

50 

01455 

68-7501 

03201 

31-2416 

04949 

20-2056 

06700 

14-9244 

10 

51 

01484 

67-4019 

03230 

30-9599 

04978 

20-0872 

06730 

14-8596 

9 

52 

01513 

66-1055 

03259 

30-6833 

05007 

19-9702 

06759 

14-7954 

8 

53 

01542 

64-8580 

03288 

30-4116 

05037 

19-8546 

06788 

14-7317 

7 

54 

01571 

63-6567 

03317 

30-1446 

050G6 

19-7403 

06817 

14-6685 

6 

55 

01600 

62-4992 

03346 

2*3  •  8823 

05095 

19-6273 

06847 

14-6059 

5 

56 

01629 

61-3829 

03376 

29-6245 

05124 

19-5156 

06876 

14-5438 

4 

57 

01658 

60-3058 

03405 

29-3711 

05153 

19-4051 

06905 

14-4823 

3 

58 

01687 

59-2659 

29-1220 

05182  19-2959 

06934 

14-4212 

2 

59 

01716 

58-2612 

03463 

28-8771 

05212  19-1879 

06963 

14-3607 

1 

60 

01746 

57-2300.  03492 

28-6363 

05241 

19-0811 

06993 

14-3007 

0 

M 

N.  Cot. 

N.  TuuT 

IN.  Cot. 

N.  Tan. 

N.  Cot 

N.  Tan. 

N.  Cot. 

N.  Tan.  ^_ 

r 

89  Degrees.  [|  88  Degrees. 

87  Degrees. 

86  Degrees.  ! 

102 


TABLE  OF  NATURAL  TANGENTS, 


4  Degrees. 

5  Degrees,  jj  6  Degrees. 

7  Degrees. 

TC 

N.  Tan.  N.  Cot. 

N.Tan. 

N.  Cot. 

N.  Tan. 

N.  Cot. 

N.Tan. 

N  Cot. 

M 

0 

06993 

14-3007 

08749 

11-4301 

10510 

9-51436 

12278 

c-14435 

60 

I 

07022 

14-2411 

08778 

11-3919 

10540 

9-48781 

12308 

8-12481 

59 

2 

07051 

14-1821 

08807 

11-3540 

10569 

9-46141 

12338 

8-10536 

58 

3 

07080 

14-1235 

08837 

11-3163 

10599 

9-43515 

12367 

8-08600  57 

4 

07110 

14-0655 

08866 

11-2789 

10628 

9-40904 

12397 

8-06674"56 

5 

07139 

14-0079 

08895 

11-2417 

10657 

9-38307 

12426 

8-04756  55 

6 

07168 

13-9507 

08925 

1  1  •  2048 

10687 

9-35724 

12456 

8-02848  54 

r 

07197 

13-8940 

08954 

11-1681 

10716 

9-33154 

12485 

8-00948  53 

8 

07227 

13-8378 

08983 

11-1316 

10746 

9-30599 

12515 

7-99058  52 

9 

07256 

13-7821 

09013 

11-0954 

10775 

9-28058 

12544 

7-97176J51 

10 

07285 

13-7267 

09042 

11-0594 

10805 

9-25530 

2574 

7-95302  50 

11 

07314 

13-6719 

09071 

11-0237 

10834 

9-23016 

2603 

7-93438  49 

12 

07344 

13-6174 

09101 

10-9881 

10863 

9-20566 

2633 

.91582  48 

13 

07373 

13-5634 

09130 

10-9528 

10893 

9-18028 

2662J   -89734 

47 

14 

07402 

13-5098 

09159 

10-9178 

10922 

9-15554 

2692 

-87895 

46 

15 

07431 

13-.4566 

09139 

10-8829 

10952 

9-13093 

2722 

•86064 

45 

16 

07461 

13-4039 

09218 

10-8483 

10981 

9-10646 

12751 

•84242 

44 

17 

07490 

13-31515 

09247 

10-8139 

11011 

9-08211 

12781 

•82428 

43 

18 

07519 

13-2996 

09277 

10-7797 

11040 

9-05789 

12810 

•80622 

42 

19 

07548 

13-2480 

09306 

10-7457 

11070 

9-03379 

12840 

•  78825 

41 

20 

07578 

13-1969 

09335 

10-7119 

11099 

9-00983 

12869 

•  77035 

40 

21 

07607 

13-1461 

09365 

10-6783 

11128 

8-98598 

12899 

•75254  39 

22 

07636 

13-0958 

09394 

10-6450 

11158 

8-96227 

12929 

•73480!  38 

23 

07665 

13  0458 

09423 

10-6118 

11187 

8-93867 

12958 

•71715  37 

24 

07695 

12-9962 

09453 

10-5789 

11217 

8-91520 

12988 

•69957  36 

25 

07724 

12-9469 

09482 

10-5462 

11246 

8-89185 

13017 

•68208 

35 

26 

07753 

12-8981 

09511 

10-5136 

11276 

8-86862 

13047 

•66466 

34 

27 

07782 

12-8496 

09541 

10-4813 

11305 

8-84551 

13076 

7-64732 

33 

28 

07812 

12-8014 

09570 

10-4491 

11335 

8-82252 

13106 

7-63005 

32 

29 

07841 

12-7536 

09600 

10-4172 

11364 

8-79964 

13136 

7-61287 

31 

30 

07870 

12-7062 

09629 

10-3854 

11394 

8-77689 

13165 

7-59575 

30 

31 

07899 

12-6591 

09658 

10-3538 

11423 

8-75425 

13195 

7-57872 

29 

32 

07929 

12-6124 

09688 

10-3224 

11452 

8-73172 

13224 

7-56176 

28 

33 

07958 

12-5660 

09717 

10-2913 

11482 

8-70931 

13254 

7-54487 

27 

34 

07987 

12-5199 

09746 

10-2602 

11511 

8-68701 

13284 

7-52806 

26 

35 

08017 

12-4742 

09776 

10-2294 

11541 

8-66482 

13313 

7-51132 

25 

36 

08046 

12-4288 

09805 

10-1988 

11570 

8-64275 

13343 

7-49465 

24 

37 

08075 

12-3838 

09834 

10-1683 

11600 

8-62078 

13372 

7-47806  23 

38 

08104 

12-3390 

09864 

10-1381 

11629 

8-59893 

13402 

7-46154  22. 

39 

08134 

12-2946 

09893 

10-1080 

11659 

8-57718 

13432 

7-44509 

21 

40 

09163 

12-2505 

09923 

10-0780 

11688 

8-55555 

13461 

7-42871  20 

41 

08192 

12-2067 

09952 

10-0483 

11718 

8-53402 

13491 

7-41240  19 

42 

08221 

12-1632 

09981 

10-0187 

11747 

8-51259 

13521 

7-39616 

18 

43 

08251 

12-1201 

10011 

9-98930 

11777 

8-49128 

13550 

7-37999  17 

44 

08280 

12-0772 

10040 

9-96007 

11806 

8-47007 

13580 

7-36389  16 

45 

08309 

12-0346 

10069  9-93101 

11836 

8-44896 

13609 

£-34786  15 

46 

08339 

11-9923 

10099J  9-90211 

11865 

8-  42795  j  13639 

7-33190 

14 

47 

08368 

11-9504 

10128  9-87338 

11895 

8-  40705;  13669 

7-31600  13 

48 

08397 

11-9087 

10158 

9-84482 

11924|  8-38625!  13698 

7-30018  12 

49 

08427 

»ll-8673 

10187 

9-81641 

11954 

8-36555;!  13728 

7-28442  11 

50 

08456 

11-8262 

10216 

9-78817 

11983 

8-344961  13758 

7-26873 

10 

51 

08485 

11-7853 

10246  9-76009 

12013 

8-32446 

13787 

7-25310 

9 

52 

08514 

11-7448 

102751  9-73217 

12042 

8-30406 

13817 

7-23754 

8 

53 

08544 

11-7045 

10305!  9-70441 

12072  8-28376;|  13846 

7-22204 

7 

54 

G8573 

11-6645 

10334  9-67680 

12101  8-26355  13876 

7-20661 

6 

55 

OS602 

11-6248 

10363J  9-64935 

12131  8-24345  13906 

7-19125 

5 

56 

08632 

1  1  •  5853 

103931  9-62-205 

12160  8-223441!  13935 

7-17594 

4 

57 

08661  11-5461 

10422!  9-59490 

12190  8-20352  13965 

7-160711  3 

58 

08690  11-5072 

10452!  9-56791 

12219  8-18370  13995 

7-14553  2 

59 

08720)  11-4685 

10481'  9-54106 

12249  8-  16398  !  14024 

7-13042  1 

60 

087491  11-4301 

10510  9-51436 

12278  8-  14^135  l  14054 

7-11537;  o 

M  IX7.  Cut.!  N.Tan. 

'N.  Cot.  N.Tan.  j  N.  Cot.  N.  T«n.  N.  Cot. 

N.  Tan. 

M 

feo  Degrees. 

84  Degrees.  ;  83  Degrees.  !;.  62  Degrees. 

TABLE  OF  NATURAL  TANGENTS. 


103 


8  Degrees. 

9  Degrees. 

10  Degrees. 

11  Degrees. 

M 

N.Tan.   N.  Cot. 

N.Tan. 

N.  Cot. 

N.Tan.   N.  Cot. 

N.Tan. 

N.  Cot.  91 

0 

14054  7-11537 

15838 

6-31375 

17633 

5-67128 

19438 

5-14455  60 

1 

14084  7-10038 

15868 

6-30189 

17663 

5-66165 

19468 

5-13658  59 

2 

14113J  7-08546 

15898 

6-29007 

17693 

5-65205 

19498 

5-12862  58 

3 

14143  7-07059 

15928 

6-27829 

17723  5-64248 

19529 

5-12069  57 

4 

14173  7-05579 

15958 

6-26655 

17753 

5-63295 

19559 

5-11279  56 

5 

14202 

7-04105 

15988 

6-25486 

17783 

5  •  62344 

19589 

5-10490  55 

6 

14232 

7-02637 

16017 

6-24321 

17813 

5-61397 

19619 

5-09704  54 

7 

14262  7-01174 

16047 

6-23160 

17843 

'  5-60452 

19649 

5-08921  53 

8 

14291  6-99718 

16077 

6  •  22003 

17873 

5-59511 

19680 

5-08139  52 

9 

14321 

6-98268 

16107 

6-20851 

17903 

5-58573 

19710 

•S-07360,51 

10 

14351 

6-96823 

16137 

6-19703 

17933 

5-57638 

19740 

5-06584  50 

11 

14381 

6-95385 

16167 

6-18559 

17963 

5-56706 

19770 

5-05809  49 

12 

14410 

6-93952 

16196 

6-17419 

17993 

5-55777 

19801 

5-Of)037j48 

13 

14440 

6-92525 

16226 

6-16283 

18023 

5-54851 

19831 

5-04267)47 

14 

14470 

6-91104 

16256 

6-15151 

18053 

5-53927 

19861 

5-03499 

46 

15 

14499 

6-89688 

16286 

6-14023 

18083 

5-53007 

19891 

5-02734 

45 

16 

14529 

6-88278 

1631(5 

6-12899 

18113 

5-52090 

19321 

5-01971 

44 

17 

14559 

6-86874 

16346 

6-11779 

18143 

5-51176 

19952 

5-01210 

43 

18 

14588 

6-85475 

16376 

6-10664 

18173 

5-50264 

19982 

5-00451 

42 

19 

14618 

6-84082 

16405 

6-09552 

18203 

5-49356 

20012 

4-9%95 

41 

20 

14648 

6-82694 

16435 

6-08444 

18233 

5-48451 

20042 

4-98940 

40 

21 

14678 

6-81312 

16465 

6-07340 

18263 

5-47548 

20073 

4-98188 

39 

22 

14707 

6-79936 

16495 

6  •  06240 

18293 

5-46648 

20103 

4-97438 

38 

23 

14737 

6-78564 

16525 

6-05143 

18323 

5-45751 

20133 

4-96690 

37 

24 

14767 

6-77199 

16555 

6-04051 

18353 

5-44857 

20164 

4-95945 

36 

25 

14796 

6-75838 

16585 

6-02962 

18383 

5-43966 

20194 

4-95201 

35 

26 

14826 

6-74483 

16615 

6-01S78 

18414 

5-43077 

20224 

4-94460 

34 

27 

14856 

6-73133 

16645 

6-00797 

18444 

5-42192 

20254 

4-93721 

33 

28 

14886 

6-71789 

16674 

5-99720 

18474 

5-41309 

20285 

4-92984 

32 

29 

14915 

6-70450 

16704 

5-98646 

18504 

5-40429 

20315 

4-9*2249 

31 

30 

14945 

6-69116 

16734 

5-97576 

18534 

5-39552 

20345 

4-91516 

30 

"31 

14975 

6-6778? 

16764 

5-96510 

18564 

5-38677 

20376 

4-90785 

29 

32 

15005 

6-66463 

16794 

5-95448 

18594 

5-37805 

20406 

4-90056 

28 

33 

15034 

6-65144 

16824 

5-94390 

18624 

5-36936 

20436 

4-89330)27 

34 

15064 

6-63831 

16854 

5-93335 

18654 

5-36070 

20466 

4-88605126 

35 

15094 

6-62523 

16884 

5-92283 

18684 

5-35206 

20497 

4  -'87882  28 

36 

15124 

6-61219 

16914 

5-91235 

18714 

5-34345 

20527 

4-87162124 

37 

15153 

6-59921 

16944 

5-90191 

18745 

5-33487 

20557 

4-86444 

23 

38 

15183 

6-58627 

16974 

5-89151 

18775 

5-32631 

20588 

4-85727 

22 

39 

15213 

6-57339 

17004 

5-88114 

18805 

5-31778 

20618 

4-85013 

21 

40 

15243 

6-56055 

17033 

5-87080 

18835 

5-30928 

20648 

4-84300 

20 

41 

15272 

6-54777 

17063 

5-86051 

18865 

5-30080 

20679 

4-83590 

19 

42 

15302 

6-53503 

17093 

5-85024 

18895 

5-29235 

20709 

4-82882 

18 

43 

15332 

6  •  52234 

17123 

5-84001 

18925 

5-28393 

20739 

4-82175 

17 

44 

15362 

6-50970 

17153 

5-82982 

18955 

5-27553 

20770 

4-81471 

16 

45 

15391 

6-49710 

17183 

5-81966 

18986 

5-26715 

20800 

4-80769 

15 

46 

15421 

6-48456 

17213 

5-80953 

19016 

5-25880 

20830 

4-80068 

14 

47 

15451 

6-47206 

17243 

5-79944 

19046 

5-25048 

20861 

4-79370 

13 

48 

15481 

6-45961 

17273 

5-78938 

19076 

5-24218 

20891 

4-78673 

12 

49 

15511 

6-44720 

17303 

5-77936 

19106 

5-23391 

20921 

4-77978 

11 

50 

15540 

6-43484 

17333 

5-76937 

19136 

5-22566 

20952 

4-77286 

10 

51 

15570 

6-42253 

17363 

5-75941 

19166 

5-21744 

20982 

4  -.76595 

9 

52 

15600 

6-41026 

17393 

5  •  74949 

19197 

5-20925 

21013 

4-75906 

8 

53 

15630 

6-39804 

17423 

5-73960 

19227 

5-20107 

21043 

4-75219 

7 

64 

15660 

6-38587 

17453 

5-72974 

19257 

5-19293 

21073 

4-74534 

6 

55 

15689 

6-37374 

17483 

5-71992 

19287 

5-18480 

21104 

4-73851 

5 

56 

15719 

6-36165 

17513 

5-71013 

19317 

5-  17671 

21134 

4-73170 

4 

57 

15749 

6-34961 

17543 

5-70037 

19347 

5-  16863 

21164 

4-72490 

3 

58 

15779 

6-33761 

17573 

.5-69064 

19378  5-16058 

21195 

4-tl8l3 

2 

59 

15809 

6-32566 

17603 

5-68094 

19408  |  5-15256 

21225 

4-71137 

1 

60 

15838 

6-31375 

17633 

5-67128 

19438  5-14455 

21256 

4-70463 

0 

M 

N.  Cot. 

N.  Tan. 

N.  Cot. 

N  Tan. 

N.  Cot   N.  Tan. 

N.  Cot. 

N.  Tan. 

M 

81  Degrees. 

80  Degrees. 

79  Degrees. 

78  Degrees. 

104 


TABLE  OF  NATURAL  TANGENTS. 


12  Degrees. 

13  Degrees. 

14  Degrees. 

15  Degrees. 

M 

N.'Can. 

N.  Tan. 

N.  Tan. 

N.  Cot. 

N.  Tan. 

N.  Cot. 

N.  Tan.  N.  Cot. 

M 

0 

21256 

4-70463 

23087 

4-33148 

24933 

4-01078 

26795!  3-73205 

60 

1 

21286 

4-69791 

23117 

4-32573 

24964 

4-00582 

26826 

3-72771 

59 

2 

21316 

4-69121 

23148 

4-32001 

24995 

4-00086 

26857 

3-72338 

58 

8 

21347 

4-63452 

23179 

4-31430 

25026 

3-99592 

26888 

3-71907 

57 

4 

21377 

4-67786 

23209 

4-30860 

25056 

3-99099 

26920 

3-71476 

56 

5 

21408 

4-67121 

23240 

4-30291 

25087 

3-98607 

26951 

3-71046 

55 

6 

21438 

4-66458 

23271 

4-29724 

25118 

3-98117 

26982 

3-70616 

54 

7 

21469 

4-65797 

23301 

4-29159 

25149 

3-97627 

27013 

3-70188 

53 

8 

21499 

4-65138 

23332 

4-28595 

25180 

3-97139 

27044 

3-69761 

52 

9 

21529 

4-64480 

23363 

4-28032 

25211 

3-96651 

27076 

3-69335 

51 

10 

21560 

4-63825 

23393 

4-27471 

25242 

3-96165 

27107 

3-68909 

50 

11 

21590 

4-63171 

23424 

4-26911 

25273 

3-95680 

27133 

3-68485 

49 

12 

21621 

4-62518, 

23455 

4-26352 

25304 

3-95196 

27169 

3-68061 

48 

13 

21651 

4-61868 

23484 

4-25795 

25335 

3-94713 

27201 

3-67638 

47 

14 

21682 

4-61219 

23516 

4-25239 

25366 

3-94232 

27232 

3-67217 

46 

15 

21712 

4-60572 

23547 

4-24685 

25397 

3-93751 

27263 

3-66796 

45 

16 

21743 

4-59927 

23578 

4-24132 

25428 

3-93271 

27294 

3-66376 

44 

17 

21773 

4-59283 

23608 

4-23580 

25459 

3-92793 

27326 

3-65957 

43 

18 

21804 

4-58641 

23639 

4-23030 

25490 

3-92316 

27357 

3-65538 

42 

19 

21834 

4-58001 

23670 

4-22481 

25521 

3-91839 

27388 

3-65121 

41 

20 

21864 

4-57363 

23700 

4-21933 

25552 

3-91364 

27419 

3-64705 

40 

21 

21895 

4-56726 

23731 

4-21387 

25583 

3-90890 

27451 

3-64289 

39 

22 

21925 

4-56091 

23762 

4-20842 

25614 

3-90417 

27482 

3-63874 

38 

23 

21956 

4-55458 

23793 

4-20298 

25645 

3-89945 

27513 

3-63461 

37 

24 

21986 

4-54826 

23823 

4-19756 

25676 

3-89474 

27545 

3-63048 

36 

25 

22017 

4-54196 

23854 

4-19215 

25707 

3-89004 

27576 

3-62636 

35 

26 

22047 

4-53568 

23885 

4-18675 

25738 

3-88536 

27607 

3-62224 

34 

27 

22078 

4-52941 

23916 

4-18137 

25769 

3-88068 

27638 

3-61814 

33 

28 

22108 

4-52316 

23946 

4-17600 

25800 

3-87601 

27670 

3-61405 

32 

29 

22139 

4-51693 

23977 

4-17064 

25831 

3-87136 

27701 

3-60996 

31 

30 

22169 

4-51071 

24008 

4-16530 

25862 

3-86671 

27732 

3-60588 

30 

31 

22200 

4-50451 

24039 

4-15997 

25893 

3-86208 

27764 

3-60181 

29 

32 

22231 

4-49832 

24069 

4-15465 

25924 

3-85745 

27795 

3-59775 

28 

33 

22261 

4-49215 

24100 

4-14934 

25955 

3-85284 

27826 

3-59370 

27 

34 

22292 

4-48600 

24131 

4-14405 

25986 

3-84824 

27858 

3*58966 

26 

35 

22322 

4-47986 

24162 

4-13877 

26017 

3-84364 

27889 

3-58562 

25 

36 

22353 

4-47374 

24193 

4-13350 

26048 

3-83904 

27920 

3-58160 

24 

37 

22383 

4-46764 

24223 

4-12825 

26079 

3-83449 

27952 

3-57758 

23 

38 

22414 

4-46155 

24254 

4-12301 

26110 

3-82992 

27983 

3-57357 

22 

39 

22444 

4-45548 

24285 

4-11778 

26141 

3-82537 

28015 

3-56957 

21 

40 

22475 

4-44942 

24316 

4-11256 

26172 

3-82083 

28046 

3  56557 

20 

41 

22505 

4-44338 

24347 

4-10736 

26203 

3-81630 

28077 

3-56159 

19 

42 

22536 

4-43735 

24377 

4-10216 

26235 

3-81177 

28109 

3-55761 

18 

43 

22567 

4-43134 

24408 

4-09699 

26266 

3-80726 

28140 

3-55364 

17 

44 

22597 

4-42534 

24439 

4-09182 

26297 

3-80276 

28172 

3-54968 

16 

45 

22628 

4-41936 

24470 

4-08666 

26328 

3-79827 

28203 

3-54573 

15 

"46 

22658 

4-41340 

24501 

4-08152 

26359 

3-79378 

28234 

3-54179 

14~ 

47 

22689 

4-40745 

24532 

4-07639 

26390 

3-78931 

28266 

3-53785 

13 

48 

22719 

4-40152 

24562 

4-07127 

26421 

3-78485 

28297 

3-53393 

12 

49 

22750 

4-39560 

24593 

4-06616 

26452 

3-78040 

28329 

3-53001 

11 

50 

22781 

4-38969 

24624 

4-06107 

26483 

3-77595 

28360 

3-52609 

10 

51 

22811 

4-38381 

24655 

4-05599 

26515 

3-77152 

28391 

3-52219 

9 

52 

22842 

4-37793 

24686  4-05092 

26546 

3-76709 

28423 

3-51829 

8 

53 

22872 

4-37207 

24717 

4-04586 

26577 

3-76268 

28454 

3-51441 

7 

54 

22903 

4-36623 

24747 

4-04081 

26608 

3-75828 

28486 

3-51053 

6 

55 

22P34 

4-36040 

24778 

4-03578 

26639 

3-75388 

28517 

3-50666 

5 

56 

22964 

4-35459 

24809  4-03075 

26670 

3-74950 

28549 

3-50279 

4 

57 

22995 

4-34879 

24840  4-02574 

26701 

3-74512 

28580 

3-49894 

3 

58 

23026 

4-34300 

24871  4-02074 

26733 

3-74075 

28612 

3-49509 

2 

59 

23056 

4-33723 

24902  4-01576 

26764 

3-73644 

28643 

3-49125 

1 

<JQ 

23087 

4-33148 

24933  4-01078 

26795 

3-73205 

2867,5 

3-48741 

0 

M 

N  Cot.  N.  Coi. 

N.  Cot.  N.Tan. 

N.  Cot. 

N.  Tan. 

N.  Cot. 

N.  Tan. 

M~ 

77  Degrees. 

76  Degrees. 

75  Degrees. 

74  Degrees. 

TABLE  OF  NATURAL  TANGENTS. 


106 


16  Degrees. 

17  Degrees. 

18  Degrees. 

19  Degrees. 

M 

N.  Tan. 

N.  Cot. 

N.Tan.  t  N.  Cot. 

N.Tan 

N.  Cot. 

N.Tan. 

N.  Cot. 

M 

0 

28675 

3-48741 

30573 

3-27085 

32492 

3-07768 

34433 

2-90421 

60 

1 

28706 

3-48359 

30605 

3-26745 

32524 

3-07464 

34465 

2-90147 

59 

2 

28738 

3-47977 

30637 

3-26406 

32556 

3-07160 

34498 

2-89873 

58 

3 

28769 

3-47596 

30669 

3-26067 

32588 

3-06857 

34530 

2-89600 

57 

4 

28800 

3-47216 

30700 

3-25729 

32621 

3-06654 

34563 

2-89327 

56 

6 

28832 

3-46837 

30732 

3-25392 

32653 

3-06252 

34596 

2-89055 

55 

6 

23864 

3-46458 

30764 

3-25055 

32685 

3-05950 

34628 

2-88783 

54 

7 

28895 

3-46080 

30796 

3-24719 

32717 

3-05649 

34661 

2-88511 

53 

8 

28927 

3-45703 

30828 

3-24383 

32749 

3-05349 

34693 

2-88240 

52 

9 

28958 

3-45327 

30860 

3-24049 

32782 

3-05049 

34726 

2-87970 

51 

10 

28990 

3-44951 

30891 

3-23714 

32814 

3-04749 

34758 

2-81700 

50 

11 

29021 

3-44576 

30923 

8-23381 

32846 

3-04450 

34791 

2-87430 

49 

12 

29053 

3-44202 

30955 

3-23048 

32878 

3-04152 

34824 

2-87161 

48 

13 

29084 

3-43829 

30987 

3-22715 

32911 

3-03854 

34856 

2-86892 

47 

14 

29116 

3-43456 

31019 

3-22384 

32943 

3-03556 

34889 

2-86624 

46 

15 

29147 

3-43084 

31051 

3-22053 

32975 

3-03260 

34922 

2-86356 

45 

16 

29179 

3-42713 

31083 

3-21722 

33007 

3-02963 

34954 

2-86089 

44~ 

17 

29210 

3-42343 

31115 

3-21392 

33040 

3-02667 

34987 

2-85822 

43 

18 

29242 

3-41973 

31147 

3-21063 

33072 

3-02372 

35019 

2-85555 

42 

19 

29274 

3-41604 

31178 

3-20734 

33104 

3-02077 

35052 

2-85289 

41 

20 

29305 

3-41236 

31210 

3-20406 

33136 

3-01783 

35085 

2-85023 

40 

21 

29337 

3-40869 

31242 

3-20079 

33169 

3-01489 

35117 

2-84758 

39 

22 

29368 

3-40502 

31274 

3-19752 

33201 

3-01196 

35150 

2-84494 

38 

23 

29400 

3-40136 

31306 

3-19426 

33233 

3-00903 

35183 

2-84229 

37 

24 

29432 

3-39771 

31338 

3-19100 

33266 

3-00611 

35216 

2-83965 

36 

25 

29463 

3-39406 

31370 

3-18775 

33298 

3-00319 

35248 

2-83702 

35 

26 

29495 

3-39042 

31402 

3-18451 

33330 

3-00028 

35281 

2-83439 

34 

27 

29526 

3-38679 

31434 

3-18127 

33363 

2-99738 

35314 

2-83176 

33 

28 

29558 

3-38317 

31466 

3-17804 

33395 

2-99447 

35346 

2-82914 

32 

29 

29590 

3-37955 

31498 

3-17481 

33427 

2-99158 

35379 

2-82653 

31 

30 

29621 

3-37594 

31530 

3-17159 

33460 

2-98868 

35412 

2-82391 

30 

31 

29653 

3-37234 

31562 

3-16838 

33492 

2-98580 

35445 

"^82130 

29 

32'  29685 

3-36875 

31594 

3-16517 

33524 

2-98292 

35477 

2-81870 

28 

33i  29716 

3-36516 

31626 

3-16197 

33557 

2-98004 

355X0 

2-81610 

27 

34!  29748 

3-36158 

31658 

3-15877 

33589 

2-97717 

3r"543 

2-81350 

26 

35 

29780 

3-35800 

31690 

3-15558 

33621 

2-97430 

35576 

2-81091 

25 

36 

29811 

3-35443 

32722 

3-15240 

33654 

2-97144 

35608 

2-80833 

24 

37 

29843 

3-35087 

31754 

3-14922 

33686 

2-96858 

35641 

2-80574 

23 

38 

29875 

3-34732 

31786 

3-14605 

33718 

2-96573 

35674 

2-80316 

22 

39 

29906 

3-34377 

31818 

3-14288 

33751 

2-96288 

35707 

2-80059 

21 

40 

29938 

3-34023 

31850 

3-13972 

33783 

2-96004 

35740 

2-79802 

20 

41 

29970 

3-33670 

31882 

3-13656 

33816 

2-95720 

35772 

2-79545  19 

42 

3U001 

3-33317 

31914 

3-13341 

33848 

2-95437 

35805 

2-79289 

18 

43 

30033 

3-32965 

31946 

3-13027 

33881 

2-95155 

35838 

2-79033  17 

44 

30065 

3-32614 

31978 

3-12713 

33913 

2-94872 

35871 

2-  78778'  '6 

45 

30097 

3-32264 

32010 

1  •  1  2400 

33945 

2-94590; 

35904 

2-78323  15 

46  30128 

3-31914 

32042 

3-12087 

33978 

2-94309, 

35937 

2-78269,14 

47 

30160!  3-31565 

32074 

3-11Z75 

34010 

2  .94028' 

35969 

2-78014  13 

48 

30192  3-31216 

32106 

3-11464 

34043 

2-93748 

36002 

2-77761:*2 

49 

30224  3-30868 

32139 

3-11153 

34075 

2-93468 

36035 

2  -77507]  11 

50 

30255 

3-30521 

32171 

3-10842 

34108 

2-93189 

36068 

2-77254  1° 

51 

30287 

3-30174 

32203 

3-10532 

34140 

2-92910 

36101 

2-77002 

9 

52 

30319  3-29829 

32235 

3-10223 

34173 

2-92632; 

36134 

2-76750 

8 

53 

30351  3-29483 

32267 

3-09914 

34205  2-92354 

36167 

2-76498  7 

54 

30382,  3-29139 

32299 

3-99606 

342381  2-92076 

36199 

2-76247  6 

55 

30414  3-28795 

32331 

3-09298 

34270  j  2-91799 

36232 

2-75996  5 

56 

30446  3-28452 

32363 

3-08991 

34303!  2-91523 

36265 

2-75746  '4 

57 

30478  3-28109 

32396 

3-08685 

34335  !  2-91246 

36298 

2-75496  3 

58 

30509  3-27767 

32428 

3-08379 

34368  2-90971! 

36331 

2-7524fi:  2 

59 

30341  3-27426 

32460 

3-08073 

34400;  2-90696, 

36364 

2-74997  1 

60 

30573  3-  27031 

32492 

3-07768 

34433  2-90421' 

36397 

2-7474H  0 

M 

N.  Cot.  N.  T;in.. 

N.  Col. 

N.  Tan.  j  N  Cot  i  N.  Tan. 

N.  Cot.l 

N.  Tan.  M_ 

73  Decrees. 

72  DesT'-es.  j  71  Decrees. 

70  Decrees. 

106 


TABLE  OF  NATURAL  TANGENTS. 


20  Degrees. 

21  Degrees. 

22  Degrees. 

23  Degrees. 

M 

N.  Tan. 

N.  Cot. 

N.Tan. 

N.  Cot. 

N.  Tan. 

N.  Cot. 

N.Tan. 

N.  Cot 

M 

0 

36397 

2-74748 

38386 

2-60509 

40403 

2-47509 

42447 

2-35585 

60 

1 

36430 

2-74499 

38420 

2-60283 

40436 

2-47302 

42482 

2-35395 

59 

2 

36463 

2-74251 

38453 

2-60057 

40470 

2-47095 

42516 

2-35205 

58 

3 

36496 

2-74004 

38487 

2-59831 

40504 

2-46888 

42551 

2-35015 

57 

4 

36529 

2-73756 

38520 

2-59606 

40538 

2-46682 

42585 

2-34825 

56 

5 

36562 

2  '73509 

38553 

2-59381 

40572 

2-46476 

42619 

2-34636 

55 

6 

36595 

2-73263 

38587 

2-59156 

40606 

2-46270 

42654 

2-34447 

54 

7 

36628 

2-73017 

38620 

2-58932 

40640 

2-46065 

42688J  2-34258 

53 

8 

36661 

2-72771 

38654 

2-58708 

40674 

2-45860 

427221  2-34069 

52 

9 

36694 

2-72526 

38687 

2-58484 

40707 

2-45655 

42757 

2-33881 

51 

10 

36727 

2-72281 

38721 

2-58261 

40741 

2-45451 

42791 

2-33693 

50 

11 

36760 

2-72036 

38754 

2-58038 

40775 

2-45246 

42826 

2-33505 

49 

12 

36793 

2-71792 

38787 

2-57815 

40809 

2-45043 

42860 

2-33317 

48 

13 

36826 

2-71548 

38821 

2-57593 

40843 

2-44839 

42894 

2-33130 

47 

14 

36859 

2-71305 

38854 

2-57371 

40877 

2-44636 

42929 

2-32943 

46 

15 

36892 

2-71062 

38888 

2-57150 

40911 

2-44433 

42963 

3-32756 

45 

16 

36925 

2-70819 

38921 

2-56928 

40945 

2-44230 

42998 

2-32570 

44 

17 

36958 

2-70577 

38955 

2-56707 

40979 

2-44027 

43032 

2-32383 

43 

18 

36991 

2-70335 

38988 

2-56487 

41013 

2-43825 

43067 

2-32197 

42 

19 

37024 

2-70094 

39022 

2-56266 

41047 

2-43623 

43101 

2-32012 

41 

20 

37057 

2-69853 

39055 

2-56046 

41081 

2-43422 

43136 

2-31826 

40 

21 

37090 

2-69612 

39089 

2-55827 

41115  2-43220 

43170 

2-31641 

39 

22 

37123 

2-69371 

39122 

2-55608 

41149  2-43019 

43205 

2-31456 

38 

23 

37157 

2-69131 

39156 

2-55389 

41183  2-42819 

43239 

2-31271 

37 

24 

37190 

2-68892 

39190 

2-55170 

41217  2-42618 

43274 

2-31086 

36 

25 

37223 

2-68653 

39223 

2-54952 

41251]  2-42418 

43308 

2-30902 

35 

26 

37256 

2-68414 

39257 

2-54734 

41285 

2-42218 

43343 

2-30718 

34 

27 

37289 

2-68175 

39290 

2-54516 

41319 

2-42019 

43378 

2-30534 

33 

28 

37322 

2-67937 

39324 

2-54299 

41353 

2-41819 

43412 

2-30351 

32 

29 

37355 

2-67700 

39357 

2-54082 

41387 

2-41620 

43447 

2-30167 

31 

30 

37388 

2-67462 

39391 

2-53865 

41421 

2-41421 

43481 

2-29984 

30 

31 

37422 

2-67225 

39425 

2-53648 

41455 

2-41223 

43516 

2-29801 

29 

32 

37455 

2-66989 

39458 

2-53432 

41430 

2-41025 

43550 

2-29619 

28 

33 

37488 

2-66752 

39492 

2-53217 

41524 

2-40827 

43555 

2-29437 

27 

34 

37521 

2-66516 

39526 

2-53001 

41558 

2-40629 

43620 

2-29254 

26 

35 

37554 

2-66281 

395591  2-52786 

41592 

2-404.32 

43654 

2-29073 

25 

36 

37588 

2-66046 

30593 

2-52571 

41620 

2-40235 

43689 

2-28891 

24 

37 

37621 

2-65811 

39626 

2-52357 

41660 

2-40038 

43724 

2-28710 

23 

38 

37654 

2-65576 

39660 

2-52142 

41694 

2-39841 

43758 

2-28528 

22 

39 

37687 

2-65342 

39694  2-51929 

41728 

2-39645 

43793 

2-28348 

21 

40 

37720 

2-65109 

39727J  2-51715 

41763 

2-39449 

43828 

2-28167 

20 

41 

37754 

2-64875 

39761  2-51502 

41797 

2-39253 

43862 

2-27987 

19 

42 

37787 

2-64642 

39795  2-51289 

41831 

2-39058 

43897 

2-27806 

18 

43 

37820 

2-64410 

39829  2-51076 

41865 

2-38862 

43932 

2-27626 

17 

44 

37853 

2-64177 

39862 

2-50864 

41899 

2-38668 

43966 

2-27447 

16 

45 

37887 

2-63945 

39896 

2-50052 

41933 

2-38473 

44001 

2-27267 

15 

46 

37920 

2-63714 

39930  2-50440 

41968 

2-38279 

44036 

2-27088 

14 

47 

37953 

2-63483 

39963  2-50229 

42002 

2-38084 

44071 

2-26909 

13 

48 

37986 

2-6325-2 

39997.  2-50018 

42036 

2-37891 

441051  2-26730 

12 

49 

38020 

2-63021 

4003  li  2-49807 

42070 

2-37697 

44140  2-26552 

11 

50 

38053 

2-62791 

40065  2-49597 

42105 

2-37504 

44175  2-26374 

10 

51 

38086 

2-62561 

40098!  2-49386 

42139 

2-37311 

44210  2-26196 

9 

52 

38120 

2-62332 

40132;  2-49177 

42173 

2-37118 

44244;  2-26018 

8 

53 

38153 

2-62103 

40166  2-48967 

42207  2-36925  44279  2-25840 

7 

54 

38186 

2-61874 

40200  2-48758 

42242  2-36733J  44314  2-25663 

6 

55 

38220 

2-61646 

40234  2-48549 

42276  2-36541  44349  2-25486 

5 

56 

38253 

2-61418 

40267  2-48340 

423  10J  2-36349  44384  2-25309 

4 

57 

38286  2-61190 

40301  2-48132 

42345;  2-36158  44418  2-25132 

3 

58 

38320!  2-60963 

40335  2-47924J  -12379,  2-35967!  44453  2-24956 

2 

§9 

38353  2-607.16 

40309.  2-47716)!  42413^  2-3577(5  44-188  2-24760j  1 

66 

38386  2-60509  40403.  2--17509J  424471  2-355S5  4-W3  2-24604  0  ] 

M  N.  Cot..  N.Tan.  S".  Col.  N.Tan.   N.  O.t.  N.  Tan.  .N.  Cot.  N.  Tan.  M 

'69  Degrees   :  08  Degrees,  li  67  Degrees,  i.  G6  Degrees. 

TABLE  OF  NATURAL  TANGENTS. 


107 


24  Degrees.  [|  25  Degrees, 

26  Degrees,  j]  27  Degrees. 

M 

N.  Tan. 

N.  Cot. 

N.Tari. 

N.  Cot. 

N.Tan. 

N.  Cot. 

N.Tan.   N.  Cot. 

M 

0 

44523 

2-24604 

46631 

2-14451 

48773 

2-05030 

50953 

•96261 

60 

1 

44558 

2-24428 

46666 

2-14288 

48809 

2-04879 

50989 

•96120 

59 

2 

44593 

2-24252 

46702 

2-14125 

48845 

2-04728 

51026 

•95979 

58 

3 

44627 

2-24077 

46737 

2«13963 

48881 

2-04577 

51063 

•95838 

57 

4 

44662 

2-23902 

46772 

2-13801 

48917 

2-04426 

51099 

-95698 

56 

5 

44697 

2-23727 

46808 

2-13639 

48953 

2-04276 

51136 

•95557 

55 

6 

44732 

2-23553 

46843 

2-13477 

48989 

2-04125 

51173 

•95417 

54 

7 

44767 

2-23378 

46879 

2-13316 

49026 

2-03975 

51209 

•95277 

53 

8 

44802 

2-23204 

46914 

2-13154 

49062 

2-03825 

51246 

•951-37 

52 

9 

44837 

2-23030 

46950 

2-12993 

490981  2-03675 

51283 

•94997 

51 

10 

44872 

2-22857 

46985 

2-12832 

49134 

2-03526 

51319 

-94858 

50 

11 

44907 

2-22683 

47021 

2-12671 

49170 

2-03376 

51356 

-94718 

49 

12 

44942 

2-22510 

47056 

2-12511 

49206 

2-03227 

51393 

•94579 

48 

13 

44977 

2-22337 

47092 

2-12350 

49242 

2-03078 

51430 

-94440 

47 

14 

45012 

2-22164; 

47128 

2-12190 

49278 

2-02929 

51467 

•94301 

46 

15 

45047 

2-21992| 

47163 

2-12030 

49315 

2-02780 

51503 

•94162 

45 

Te 

45082 

2-21819 

47199 

2-11871 

49351 

2-02631 

51540 

•  94023 

44 

17 

45117 

2-21647 

47234 

2-11711 

43387 

2-02483 

51577 

-9-3885 

43 

18 

45152 

2-21475 

47270 

2-11552 

49423 

2-02335 

51614 

-  93746 

42 

19 

45187 

2-21304' 

47305 

2-11392 

49459 

2-02187 

61651 

•  93608 

41 

20 

45222 

2-21  1321 

47341 

2-11233 

49495 

2-  02039 

51688 

•93470 

40 

21 

45257 

2-20961 

47377 

2-11075 

49532 

2-01891 

51724 

-93332 

39 

22 

45292 

2-20790i 

47412 

2-10916 

49568 

2-01743 

51761 

•93197 

38 

123 

45327 

2-206191 

47448 

2-10758 

49604 

2-01596 

51798 

•93057 

37 

24 

45362 

2-20449 

47483 

2-10600 

49640 

2-01449 

51835 

•92920 

36 

25 

45397 

2-20278 

47519 

2-10441 

49677 

2-01302 

51872 

-92782 

35 

26 

45432 

2-20108! 

47555 

2-  10284 

49713 

2-01155 

51909 

•92645 

34 

27 

45467 

2-19938 

47590 

2-00126 

49749 

2-01008 

51946 

•92508 

33 

•28 

45502 

2-19769 

47626 

2-09969 

49786 

2-00862 

51983 

•92371 

32 

29 

45537 

2*-  19599 

47662 

2-09811 

49822 

2-00715 

52020 

•92235 

31 

30 

45573 

2-19430 

4769? 

2-09654 

49858 

2-00569 

52057 

•92098 

30 

~3l 

45608 

2-19261 

47733 

2-09498 

^49894 

2-00423 

52094 

•91962 

29~ 

32 

45643 

2-19092 

47769 

2-09341 

49931 

2-00277 

52131 

•91825 

28 

33 

45678 

2-18923 

47805 

2-09184 

49967 

2-00131 

52168 

•91690 

27 

34 

45713 

2-18755 

47840 

2-09028 

50004 

1-99986 

52205 

•91554 

26 

35 

45748 

2-18587 

47876 

2-08872 

50040 

•99841 

52242 

•91418 

25 

36 

45784 

2-18419 

47912 

2-08716 

50076 

•99695 

52279 

•91282 

24 

37 

45819 

2-18251 

47948 

2-08560 

50113 

•99550 

52316 

•91148 

23 

38 

45854 

2-18084 

47984 

2-08405 

50149 

•99406 

52353 

1-91017 

22 

39 

45889 

2-17916 

48019 

2-08250 

50185 

•99261 

52390 

1-90876 

21 

40 

45924 

2-17749 

48055 

2-08094 

50222 

-99116 

52427 

1-90741 

20 

41 

45960 

2-17582 

48091 

2-07939 

50258 

.98972 

52464 

1-90607 

19 

42 

45995 

2-17416 

48127 

2-07785 

50295 

-  98828 

52501 

1-90472 

18 

43 

46030 

2-17249 

48163 

2-07630 

50331 

-98684 

52538 

1-90337 

17 

44 

46065 

2-17083 

48198 

2-07476 

50368 

-98540 

52575 

1-90203 

16 

45 

46101 

2-16917 

48234 

2-07321 

50404 

•98396 

52613 

1-90069 

15 

46 

45136 

2-16751 

48270 

2-07167 

50441 

•98253 

52650 

1-89935 

14 

47 

46171 

2-16585 

48306 

2-07014 

50477 

•98110 

52687 

1-89801 

13 

48 

46206 

2-16420 

43342 

2-06860 

50514 

•97966 

52724 

1-89667 

12 

49 

46242 

2-16255 

48378 

2-06706 

50550 

-97823 

52761 

1-89533 

11 

50 

46277 

2-16090 

48414 

2-06553 

50587 

•97680 

52798 

1-891400 

10 

51 

46312 

2-15925 

48450 

2-06400 

50623 

•97538 

52836 

1-89266 

9 

52 

46348 

2-15760 

48486 

2-06247 

50660 

•97395 

52873 

1-89133 

8 

53 

46383 

2-15596 

48521 

2-06094 

50696 

•  97253 

52910 

1-89000 

7 

54 

46418 

2-15432 

48557 

2-05942 

50733 

•97111 

52947 

1-88867 

6 

55 

46454 

2-15268 

48593  2-05789 

50769 

•96969 

52984 

•88734 

5 

56 

46489 

2-15104 

48629  2-05637 

50806   •  96827 

53024 

•88602 

4 

57 

46525 

2-14940 

48665^  2-05485 

50843   -96685 

53059 

•88469 

3 

•8 

46560 

2-14777 

48701  2-05333 

50879;   -96J544 

53096 

•8833/1  2 

59 

46595 

2-14614 

48737  2-05182 

50916   -96402 

53134 

•88205 

1 

60 

46631 

2-14451 

4S773  2-05030 

50953:   -96261 

53171 

1-88073 

0 

~M. 

N.  Cot. 

N.  Tan. 

N.  Cot.  N.  Tan. 

N.  Cot   N.  Tan.  ;N.  Cot. 

N.  Tan. 

M 

65  Degr  °s. 

G4  Decrees. 

63  Degrees.  U  62  Degrees. 

J5 

109 


TABLE  OF  NATURAL  TANGENTS. 


28  Degrees. 

29  Degrees. 

30  Degrees. 

31  Degrees. 

M 

N.  Tan. 

N.  Cot. 

N.Tan. 

N.  Cot. 

N.  Tan. 

N.  Cot. 

N.  Tan 

N.  Cot. 

M 

0 

53171 

1-88073 

55431 

1-80405 

57735 

1-73205 

60086 

1-66428 

60 

1 

53208 

1-87941 

55469 

1-80281 

57774 

1-73089 

60126 

1-66318 

59 

2 

53246 

1-87809 

55507 

1-80158 

57813 

1-77973 

60165 

1-66209 

58 

3 

53283 

-87677 

55545 

1-80034 

57851 

1-72857 

60205 

1-66099 

57 

4 

53320 

•87546 

55583 

1-V9911 

57890 

1-72741 

60245 

1-65990 

56 

5 

53358 

-87415 

55621 

1-79788 

57929 

1-72625 

60284 

1-65881 

55 

6 

53395 

•87283 

55659 

-79665 

57968 

1  •  72509 

60324 

1-65772 

54 

7 

53432 

-87152 

55697 

•79542 

58007 

1-72393 

60364 

1-65663 

53 

8 

53470 

1-87021 

55736 

•79419 

58046 

1-72278 

60403 

1-65554 

52 

9 

53507 

1-86891 

55774 

•79296 

58085 

•72163 

60443 

1-65445 

51 

10 

53545 

1-86760 

55812 

•79174 

58124 

•  72047 

60483 

1-95337 

50 

11 

53582 

1-86630 

55850 

•79051 

58162 

•71932 

60522 

•65228 

49 

12 

53620 

1-86499 

55888 

•78929 

5820ll   -71817 

60562 

•65120 

48 

13 

53657 

1-86369 

55926 

•  78807 

58240 

•71702 

60602 

•65011U7 

14 

53694 

1-86239 

56964 

•78685 

58279 

•71588 

60642 

•64903 

46 

15 

53732 

1-86109 

56003 

•78563 

58318 

•71473 

60681|   -64795 

45 

16 

53769 

1-85979 

56041 

•78441 

58357 

•71358 

60721 

•64687 

44 

17 

53807 

1-85850 

56079 

•78319 

58396 

•71244 

60761 

•64579 

43 

18 

53844 

1-85720 

56117 

-78198 

58435 

•71129 

60801 

•64471 

4-2 

19 

53882 

1-75591 

56156 

•78077 

58474 

•71015 

60841 

•64363 

41 

20 

53920 

1-85462 

56194 

•77955 

58513 

•70901 

60881 

•64256 

40 

21 

53957 

1-85333 

56232 

•  77834 

58552 

•70787 

60921 

•64148 

39 

22 

53995 

1-85204 

56270 

•77713 

58591 

•70673 

60960 

•64041  38 

2? 

54032 

1-85075 

56309 

•77592 

58631 

•  70560 

61000 

•63933137 

24 

54070 

•84946 

56347   -77471 

58670 

•  70446 

61040 

•63826  36 

25 

54107 

•84818 

56385   -77351 

58709 

•  70332 

61080 

•63719 

35 

26 

54145 

•84689 

56424 

•77230 

58748 

•70219 

61120 

•63612 

34 

27 

54183 

•84561 

56462 

•77110 

58787 

•70106 

61160 

•63505 

33 

28 

54220 

•84433 

56500   -76990 

58826 

•79992 

61200   -6339832 

29 

54258 

•84305 

56539!   -76869 

58865 

•69879 

61240   -6329231 

30 

54296 

•84177 

56577|   -76749 

58904 

•69766 

61280   -63185 

30 

~31 

54333 

•84049 

56616  1-76629 

58944 

•  69653 

61320   -63079 

29 

32 

54371 

•83922 

56654 

1-76510 

58983 

•69541 

61360   -62972 

28 

33 

54409 

•83794 

56693 

1-76390 

59022 

•69428 

61400;   -62866 

27 

34 

54446 

•83667 

56731   -76271 

59061 

•69315 

61440   -62760 

26 

35 

54484 

•83540 

56769   -76151 

59101 

•69203 

61480   -62654 

25 

36 

54522 

•83413 

56808   -76032 

59140 

1-69091 

61520   -62548 

24 

37 

54560 

•83286 

56846   -75913 

59179 

1-68979 

61561!   -62442 

23 

38 

54597 

•83159 

56885'   -75794 

59218 

1-68866 

61601 

•62336 

22 

39 

54635 

•83033 

56923i   -75675 

59258 

1-68754 

61641 

•62230 

21 

40 

54673 

•82906 

57962  !   -75556 

59297 

1-68643 

61681 

•62125 

20 

41 

54711 

•82780 

57000   -75437 

59336 

1-68531 

61721 

•62019 

19 

42 

54748 

1-82654 

57039  '   -75319 

59376 

1-68419 

61761 

•61914 

18 

43 

54786 

1-82528 

57078   -75200 

59415 

1-6&308 

61801 

•61808 

17 

44 

54824 

1-82402 

57116   -75082 

59454 

1-68196 

61842 

•61703 

16 

45 

•  5486.2 

1-82276 

57155   -74964 

59494 

1-68085 

61882 

•61598 

15 

46 

54900 

1-82150 

57193   -74846 

59533 

1-67974 

61922   -61493 

14 

47 

54938 

1  •  82025 

57232   -74728 

59573 

1-67869 

61962   -61388 

13 

48 

54975 

•81899 

5727]   1-74610 

59612 

1-67752 

62003'   -61283 

12 

49 

55013 

•81774 

57309  1-74492 

59651 

1-67641 

62043   -61179 

11 

50 

55051 

•81649 

57348  1-74375 

59691 

1-67530 

62083   -61074 

10 

51 

55089 

•81524 

57386  1-74257 

59730 

1-67419 

62124   -60970 

9 

52 

55127 

•81399 

57425   -74140 

59770 

1-67309 

62164   -60865 

8 

53 

55165 

•81274 

57464   -74022 

59309 

1-67198 

62204   -60761 

7 

54 

55203 

1-81150 

57503   -73905 

59849 

1-67088 

62245   -60657 

6 

55 

55241 

1-81025 

57541   -73788 

59888 

1-66978 

62285   -60553 

5 

56 

55279 

1-80901 

57580   -73671 

59928 

1-66867 

62325   -60449 

4 

57 

55317 

1-80777 

5?6l'9   -73555 

59967 

1-66757 

62366   -60345 

3 

58 

55355 

1-80653 

57657   -73438 

60007 

1-66647 

62406   -6024* 

2 

59 

55393 

1-80529 

57696   -73321 

60046 

1-66538 

62446   -60137 

1 

60 

55431 

1  •  80405 

57735   •  73205 

60086 

1-66428 

62487   -60033 

0 

M 

N.  Cot. 

N.  Tan. 

N.  Cot.  N.Tan. 

N.  Cot. 

N.  Tan. 

N.  Cot.  '  N.  Tan. 

M 

61  Degrees. 

60  Decrees. 

59  Degrees. 

58  Degrees. 

TABLE  OF  NATURAL  TANGENTS. 


109 


!  32  Degrees. 

33  Degrees. 

34  Degrees. 

35  Degrees. 

M|N.Tao.j  N.  Cot.  <  N.Tan. 

N.  Cot. 

N.Tan. 

N.  Cot. 

N.Tan. 

N.  Cot. 

M 

0 

62487:  1-60033  64941 

1-53986 

67451 

1-48256 

7U021 

1-42815 

60~ 

1 

62527  1-  59930  j  64982 

1-53888 

67493 

1-48163 

70064 

1-42726 

59 

2 

62568  1-59826 

65023 

1-53791 

67536 

1-48070 

70107 

1-42638 

58 

3 

62608!  1-59723 

65065 

1-53693 

67578 

1-47977 

70151 

1-42550 

57 

4 

62649  1-59620 

65106 

1-53595 

67620 

1-47885 

70194 

1-42462 

56 

5 

62689,  1-59517 

65148 

1-53497 

67663  1-47792 

70238 

1-42374 

55 

6 

62730|  1-59414 

65189 

1-53400 

67705 

1-47699 

70281 

1-42286 

54 

7 

62770 

1-59311 

65231 

1  •  53302 

67748 

1-47607 

70325 

1-42198 

53 

8 

62811 

1-59203 

65272 

1  •  53205 

67790 

1-47514 

70368 

1-42110 

52 

9 

62852  1-59105 

65314 

1-53107 

67832 

1-47422 

70412 

1-42022 

51 

10 

62892 

1  •  59002 

65355 

1-53010 

67875 

1-47330 

70455 

1-41934 

50 

11 

62933 

1-58900  65397 

1-52913 

67917 

1-47238 

70499 

1-41847 

49 

12 

62973 

1  -58797]  65438 

1-52816 

67960 

•47146 

70542 

1-41759 

48 

13 

63014 

1-58695  65480 

1-52719 

68002 

•47053 

70586 

1-41672 

47 

14 

63055!  1-585931  65521 

•52622 

68045 

.46962 

70629 

1-41584 

46 

15 

63U95  1-  58490  j  65563 

•52525 

68088 

•46870 

70673 

1-41497 

45 

7e 

63136 

1-58388  1  65604 

•52429 

68130 

•46778 

70717 

1-41409 

44 

17 

63177 

1-58286' 

65646 

•  52332 

68173 

•46686 

70760 

1-41322 

43 

18 

63217  1-58184 

65688 

•  52235 

68215 

•46595 

70804 

1-41235 

42 

19 

63258 

1-58083 

65729 

•52139 

68258 

•46503 

70848 

1-41148 

41 

20 

63299 

1-57981 

65771 

•52043 

68301 

•46411 

70891 

1-41061 

40 

21 

63340 

1-57879 

65813 

•51946 

68343 

•46320 

70935 

1-40974 

39 

22 

63380 

1-57778 

65854 

•51850 

68386 

•46229 

70979 

1-40887 

38 

23 

63421 

1-57676 

65896 

•51754 

68429 

•46137 

71023 

1-40800 

37 

24 

63462 

1-575751 

65938 

1-51658 

68471 

•46046 

71066 

1-40714 

36 

25 

63503 

1-57474 

65980 

1-51562 

68514 

•45955 

71110 

1-40627 

35 

26 

63544 

1-57372 

66021 

1-51466 

68557 

•45864 

71154 

1-40540 

34 

27 

63584 

1-57271 

66063 

1-51370 

68600 

•45773 

71198 

1-40454 

33 

28 

63625 

1-57170 

66105 

1-51275 

68642 

•45682 

71242 

1-40368 

32 

29 

63666 

1-570691 

66147 

1-51179 

68685 

•  45592 

71285 

1-40281 

31 

30 

63707 

1-56969; 

66189 

1-51084 

68728 

•45501 

71329 

1-40195 

30 

31 

637481  1-56868 

66230 

1-50988 

68771 

•454  10 

71373 

1-40109 

29 

32 

63789|  1-56767 

66272 

1-50893 

68814 

•45320 

71417 

1-40022 

28 

33 

63830J  1-56667 

66314 

1-50797 

68857 

•  45229 

71461 

1-39936 

27 

34 

63871  1-56566 

66356 

•50702 

68900 

•45139 

71505 

1-39850 

26 

35 

63912  1'56466 

66398 

•50607 

68942 

-45048 

71549 

1-39764 

25 

36 

63953  1-56366 

66440 

•50512 

68985 

•44958 

71593 

1-39679 

24 

37 

63994 

1-56265 

66482 

•50417 

69028 

-44868 

71637 

1-39593 

23 

38 

64035 

1-56165 

66524 

•50322 

69071 

-44778 

71681 

1-39507 

22 

39 

64076 

1-56065!  66566 

•  50228 

69114 

•44688 

71725 

1-39421 

21 

40 

64117 

1-55966 

66608 

•50133 

69157 

•44598 

71769 

1-39336 

20 

41 

64158 

1-55866 

66650 

-50038 

69200 

•44508 

71813 

1-39250119 

42 

61199 

1-55766 

66692 

1-49944 

69243 

•44418 

71857 

1-39165 

18 

43 

64240 

1-55666!  66734 

1-49849 

69286 

•44329 

71901 

1-39079 

17 

44 

64281 

1-55567  66776 

1-49755 

69329 

•44239 

71946 

1-38994 

16 

45 

64322 

1-55467 

66818 

1-49661 

69372   -44149 

71990 

1-38909 

15 

46 

64363 

•55368  66860 

1-49566 

69416   -44060 

72034 

1-38824)14 

47 

64404 

•55269,  66902 

1-49472 

69459   -43970 

72078 

1-38738 

13 

48 

64446 

•55170  66944 

1-49378 

69502 

•43881 

72122 

1-38653 

12 

49 

64487 

-55071 

66986 

1  •  49284 

69545 

•43792 

72166 

1-38568 

11 

50 

64528 

•54972 

67028 

1-49190 

69588   -43703 

72211 

1-38484 

10 

51 

64569 

•54873 

67071 

1-49097 

69631   -43614 

72255 

1-38399 

9 

52 

64610   -547741  67113 

1-49003 

69675   -43525 

72299 

1-38314 

8 

53 

64652 

•54675  67155 

•48909 

69718   -43436 

72344 

1-38229 

7 

54 

64693 

•54576  67197 

•48816 

69761   -43347 

72388 

1-38145 

6 

55 

64734 

1-544781  67239 

•48722 

69804J   -43258 

72432 

1  •  38060 

5 

56 

64775 

1-54379;  67282 

•48629 

69847   -43169 

72477 

1-37976 

4 

57 

64817 

1-54281  1|  67324 

•48536 

69891   -43080 

72521 

1-37891 

3 

58 

64858 

•541831  67366 

•48442 

69934'   -42992 

72565 

1-37807 

2 

59 

64899 

•54085J 

67409 

-48349 

69977!   -42903 

72610 

1-37722 

1 

60 

64941 

•53986! 

67451 

•48256 

70021   -42815 

72654 

1-37638 

0 

M 

N.  Cot. 

N.Tan.  | 

N.  Cot. 

N.  Tan. 

N.  Cot^  N.  Tan..  JN.  Cot. 

N.  Tan. 

M 

57  Degree*. 

5i)  Degrees. 

55  Degrees,  n  54  Degrees. 

110 


TABLE  OF  NATURAL  TANGENTS. 


36  Degrees. 

37  Degrees. 

38  Degrees. 

39  Degrees. 

M 

M.  Tan. 

N.  Cot. 

N.  Tan. 

N.  Cot. 

N.Tan. 

N.  Cot. 

N.  Tan. 

N.  Cot. 

M 

0 

72654 

1-37638 

75355 

1-32704 

78129 

1-27994 

80978 

1-23489 

0 

1 

72699 

1-37554 

75401 

1-32624 

78175 

1-27917 

81027 

1-23416 

9 

2 

72743 

1-37470 

75447 

1-32544 

78222 

1-27841 

81075 

1-23343 

8 

72788 

1-37386 

75492 

1-32464 

78269 

1-27764 

81123 

1-23270 

7 

£ 

72832 

1-37302 

75538 

1-32384 

78316 

1-27688 

81171 

1-23196 

56 

5 

72877 

1-37218 

75584 

1-32304 

78363 

1-27611 

81220 

1-23123 

5 

6 

72921 

1-57134 

75629 

1-32224 

78410 

1-27535 

81268 

1-23050 

o4 

7 

72966 

1-37050 

75675 

1-32144 

78457 

1-27458 

81316 

1-22977 

53 

8 

73010 

1-36967 

75721 

1-32064 

78504 

1-27382 

81364 

1-22904 

52 

9 

73055 

1-36883 

75767 

1-31984 

78551 

1-27306 

81413 

1-22831 

51 

10 

73100 

1-36800 

75812 

1-31904 

78598 

1-27230 

81461 

1-22758 

50 

11 

73144 

1-36716 

75858 

1-31825 

78645 

1-27153 

81510 

1-22685 

49 

12 

73189 

1-36633 

75904 

1-31745 

78692 

1-27077 

81558 

1-22612 

48 

13 

73234 

1-36549 

75950 

1-31666 

78739 

1-27001 

81606 

1-22539 

47 

14 

73278 

1*36466 

75996 

1-31586 

78786 

1-26925 

81655 

1-22467 

46 

15 

73323 

1-36383 

76042 

1-31507 

78834 

1-26849 

81703 

1-22394 

45 

16 

~73368 

1-36300 

76088 

1-31427 

78881 

1-26774 

81752 

1-22321 

44 

17 

73413 

1-36217 

76134 

1-31348 

78928 

1-26698 

81800 

1-22249 

43 

18 

73457 

1-36133 

76180 

1-31269 

78975 

1-26622 

81849 

1-22176 

42 

19 

73502 

1-36051 

76226 

1-31190 

79022 

1-26546 

81898 

1-22104 

41 

20 

73547 

1-35968 

76272 

1-31110 

79070 

1-26471 

81946 

1-22031 

40 

21 

73592 

1-35885 

76318 

1-31031 

79117 

1-26395 

81995 

1-21959 

39 

22 

73637 

1-35802 

76364 

1-30952 

79164 

1-26319 

82044 

1-21886 

38 

23 

73681 

1-35719 

76410 

1-30873 

79212 

1-26244 

82092 

1-21814 

37 

24 

73726 

1-35637 

76456 

1-30795 

79259 

1-26169 

82141 

1-21742 

36 

25 

73771 

1-35554 

76502 

1-30716 

79306 

1-26093 

82190 

1-21670 

35 

26 

73816 

1-35472 

76548 

1-30637 

79354 

1-26018 

82238 

1-21598 

34 

27 

73816 

1-35389 

76594 

1-30558 

79401 

1-25943 

82287 

1-21526 

33 

28 

73906 

1-35307 

76640 

1-30480 

79449 

1-25867 

82336 

1-21454 

32 

29 

73951 

1-35224 

76686 

1-30401 

79496 

1-25792 

82385 

1-21382 

31 

30 

73996 

1-35142 

76733 

1-30323 

79544 

1-25717 

82434 

1-21310 

30 

31 

74041 

1-35060 

76779 

1  •  30244 

79591 

1-25642 

82483 

1-21238 

29 

32 

74086 

1-34978 

76825 

1-30166 

79639 

1-25567 

82531 

1-21166 

28 

33 

74131 

1-34896 

76871 

1-30087 

79686 

1-25492 

82580 

1-21094 

27 

34 

74176 

1-34814 

76918 

1-30009 

79734 

1-25417 

82629 

1-21023 

26 

35 

74221 

1-34732 

76964 

1-29931 

79781 

1-25343 

82678 

1-2095 

25 

36 

74267 

1-34650 

77010 

1-29853 

79829 

1-25268 

82727 

1-20879 

24 

37 

74312 

1-34568 

77057 

1-29775 

79877 

1-25193 

82.776 

1-20808 

23 

38 

74357 

1-34487 

77103 

1-29696 

79-924 

1-25118 

8282.5 

1-20736 

22 

39 

74402 

1-34405 

77149 

1-29618 

79972 

1-25044 

82874 

1-20665 

21 

40 

74447 

1-34323 

77196 

1-29541 

80020 

1-24969 

82923 

1-20593 

20 

41 

74492 

1-34242 

77242 

1-29463 

80067 

1-24895 

82972 

1-20522 

19 

42 

74538 

1-34160 

77289 

1  •  29385 

80115 

1-24820 

83022 

1-2045 

18 

43 

74583 

1-34079 

77335 

1-29307 

80163 

1-24746 

83071 

1-2037 

17 

44 

74628 

1-33998 

77382 

1-29229 

802  ll 

1-24672 

83120 

1-20308 

16 

45 

74674 

1-33916 

77428 

1-29152 

80258 

1-24597 

83169 

1-2023 

15 

46 

74719 

1-33835 

77475 

1-29074 

80306 

1-24523 

83218 

1-2016 

14 

47 

74764 

1-33754 

77521 

1-28997 

80354 

1-24449 

83268 

1-2009 

13 

48 

74810 

1-33673 

77568 

1-28919 

80402 

1-24375 

83317 

1-2002 

12 

49 

74855 

1-33592 

77615 

1-28842 

80450 

1-2430 

83366 

1-1995 

11 

50 

74900 

1-3351 

77661 

1-28764 

80498 

1-24227 

83415 

1-1988 

10 

51 

74946 

1-3343 

77708 

1-2868 

80546 

1-24153 

83465 

1-1981 

9 

52 

74991 

1-3334 

77754 

1-2861 

80594 

1-24079 

83514 

1-1974 

8 

53 

75037 

1-3326 

77801 

1-2853 

80642 

1-24005 

8356 

1-19663 

7 

54 

75082 

1-3318 

77848 

1-2845 

80690 

1-2393 

8361 

1-1959 

6 

55 

75128 

1-3310 

77895 

1-2837 

80738 

1-23858 

83662  1-1952 

5 

56 

75174 

1  •  3302 

77941 

1-2830 

80786 

1-2378 

83712 

1-1945 

4 

57 

75219 

1-3294 

77988 

1-2822 

80834 

1-2371 

83761 

1-1938 

3 

58 

75264 

1-3286 

77035  1-2814 

80882 

1-2363 

83811  1-1931 

2 

59 

7531C 

1-3278 

77082!  1-2807 

80930 

1-2356 

838601  1-1924 

1 

60 

75355 

1-3270 

77129  '  1-2799 

80978 

1-2349 

83910;  1-1917 

0 

M 

N.  Cot.  I  N.Tan. 

N.  Cot.;  N.Tan. 

N.  Cot.1  N.  Tan. 

IN.  Cot.  1  N.  Tan. 

M 

53  Degrees. 

53  Degrees. 

51  Degrees. 

50  Degrees. 

TABLE  OF  NATURAL  TANGENTS. 


Ill 


40  Degrees. 

41  Degrees. 

42  Degrees. 

43  Degrees. 

M 

N.  Tan. 

N.  Cot. 

N.  Tan.  N.  Cot. 

N.  Tan. 

N.  Cot 

N.Tan. 

N.  Cot. 

M 

0 

83910 

1-19175 

S6929 

1-15037 

90040 

•11061 

93252 

1-07237 

60 

1 

83960 

1-19105 

86980 

1-14969 

90093 

•10996 

93306 

1  -071741,59 

2 

84009 

1-19035 

87031 

1-14902 

90146 

•10931 

93360 

1-07112 

58 

3 

84059 

1-18964 

87082 

1-14834 

90199 

-10867 

93415 

1-07049 

57 

4 

84108 

1-18894 

87133 

1-14767 

90251 

-10802 

93469 

•06987 

56 

5 

84158 

1-18824 

87184 

1-14699 

90304 

-10737 

93524 

•06925 

55 

6 

84208 

1-18754 

87236 

1-14632 

90357 

•10672 

93578 

•06862 

54 

7 

84258 

1-18684 

87287 

1-14565 

90410 

•10607 

93633 

•06800 

53 

8 

84307 

1-18614 

87338 

1-14498 

90463 

•10543 

93688 

•06738  52 

9 

8435? 

1-18544 

87389 

1-14430 

90516 

•10478 

93742 

•06676:51 

10 

84407 

1-18474 

87441 

1-14363 

90569 

•10414 

93797 

•06613 

50 

li 

84457 

1-18404 

87492 

1-14296 

90621 

•10349 

93852 

•06551 

49 

12 

84507 

1-18334 

87543 

1-14229 

90674 

-10285 

93906 

•06489 

48 

13 

84556 

1-18264 

87595 

1-14162 

90727 

•  10220 

93961 

•06427 

47 

14 

84606 

1-18194 

87646 

1-14095 

90781 

•10156 

94016 

•06365 

46 

15 

84656 

1-18125 

.  87698 

1-14028 

90834 

•10091 

94071 

•06303 

45 

~16 

84706 

1-18055 

87749 

1-13961 

90887 

•  10027 

94125 

•06241 

44 

17 

84756 

1-17986 

87801 

1-13894 

90940 

•09963 

94180 

•06179 

43 

18 

84806 

1-17916 

87852 

1-13828 

90993 

•09899 

94235 

•06117 

42 

19 

84856 

1-17846 

87904 

1-13761 

91046 

•09834 

942pO 

•06056 

41 

20 

84906 

1-17777 

87955 

1-13694 

91099 

•09770 

94345 

•05994 

40 

21 

84956 

1-17708 

88007 

1-13627 

91153 

•09706 

94400 

•05932 

39 

22 

85006 

1-17638 

88059 

1-13561 

91206 

•09642 

94455 

1-05870 

38 

23 

85057 

1-17569 

88110 

1-13494 

91259 

-09578 

94510 

1-05809 

37 

24 

85107 

1-17500 

88162 

1-13428 

91313 

1-09514 

94565 

1-05747 

36 

25 

85157 

1-17430 

88214 

1-13361 

91366 

1-09450 

94620 

1-05685 

35 

26 

85207 

1-17361 

88265 

1-13295 

91419 

1-09386 

94676 

1-0562434 

27 

85257 

1-17292 

88317 

1-13228 

91473 

'1-09322 

94731 

1-05562 

33 

28 

85307 

1-17223 

88369 

1  -13162 

91526 

•09258 

94786 

1-05501 

32 

29 

85358 

1-17154 

88421 

1-13096 

91580 

•09195 

94841 

•05439 

31 

30 

85408 

1-17085 

88473 

1-13029 

91633 

•09131 

94896 

•05378 

30 

31 

85458 

1-17016 

S8524 

1-12963 

91687 

•09067 

94952 

•05317 

29 

32 

85509 

1-  16947 

88576 

1-12897 

91740 

•09003 

95007 

•05255 

28 

33 

85559 

1-16878 

88628 

1-12831 

91794 

•08940 

95062 

•05194 

27 

34 

85609 

1-16809 

88680 

1-12765 

91847 

•08876 

95118 

•05133 

26 

35 

85660 

1-16741 

88732 

1-12699 

91901 

•08813 

95173 

•05072 

25 

36 

85710 

1-16672 

88784 

1-12633 

91955 

•08749 

95229 

•05010 

24 

37 

85761 

1-  16603 

88836 

1-12567 

92008 

•08686 

95284 

•04949 

23 

38 

85811 

1-  16535 

88888 

1-12501 

92062 

•08622 

95340 

•04888 

22 

39 

85862 

1-16466 

88940 

1-12435 

92116 

•08559 

95395 

•04827 

21 

40 

85912 

1-16398 

88992 

1-12369 

92170 

•08496 

95451 

•04766 

20 

41 

85963 

1-16329 

89045 

1-12303 

92223 

•08432 

95506 

•04705 

19 

42 

86014 

1-16261 

89097 

1-12238 

92277 

•08369 

95562 

•04644 

18 

43 

86064 

1-16192 

89149 

1-12172 

92331 

•08306 

95618 

•04583;  17 

44 

86115 

1-16124 

89201 

1-12106 

92385 

-08243 

95673 

•04522  16 

45 

86166 

1-16056 

89253  1-12041 

92439 

•08179 

957291   -04461 

15 

46 

86216 

1-15987 

89306  1-11975 

92493 

•08116 

95785 

1-04401 

u" 

47 

86267 

1-15919 

89358  1-11909 

92547 

•08053 

95841 

1-04340  13 

48 

86318 

1-15851 

89410  1-11844 

92601 

•07990 

95897 

1-04279  12 

49 

86368  1-15783 

89463  1-11778 

92655 

•07927 

96952  1-0421811 

50 

86419 

1-15715 

89515  1-11713 

92709 

•07864 

96008  1-04158  10 

51 

86470 

1-15647 

89567 

1-11648 

92763 

•07801 

96064:  1-04097 

9 

52 

86521 

1-15579 

89620 

1-11582 

92817 

-07738 

96120  1-04036 

3 

53 

86572 

1-15511 

896721  1-11517 

92872 

•07676 

96176  1-03976 

7 

54 
55 

86623 
86674 

1-15443 
1-15375 

89725  1-11452 
89777J  1-11387 

92926 
92980 

•07613 
1-07550 

96232  1-03915 
96288  1-03855 

6 
5 

56 

86725 

1-15308 

89S301  1-11321 

93034 

1-07487 

96344  1-03794 

4 

57 

86776 

1-15240 

89883  1-1*1256 

93088 

1-07425 

96400  1-03734 

3 

58 

86827 

1-15172 

89935  1-11191 

93143 

1-07362 

96457  1-03674 

2 

59 

86878 

1-15101 

89988  1-11126 

93197 

1-07299  96513  1-03613 

1 

60  86929  1-15037]  'J0040  1-11061 

93252 

1-07237;  96569  1-03553 

0 

M 

N.  Cot.1  N.Tan.  N.  Cot._  N.Tan. 

N.  Cot. 

N.  Tan.  N.  Cot.  N.  Tan. 

»« 

I-TTI 

49  Decrees.  '•!  48  Degrees. 

47  Degrees.  -  4o  Degrees. 

112 


TABLE  OF  NATURAL  TANGENTS. 


44  Degrees.  | 

44  Degrees. 

M 

\.  Tan. 

N.  Cot.   M 

M 

N.  Tan. 

N.  Cot. 

M 

~0 

96569 

1-03553'eO 

31 

98327 

•01702 

29 

I 

96625 

1-03493:59 

32 

98384 

•01642 

28 

2 

96681 

1-03433  \58 

33 

98441 

•01583 

27 

3 

96738 

1-03372  57 

34 

98499 

•01524 

26 

4 

96794 

1-0331256 

35 

98556 

•01465 

2& 

5 

96850 

1-0325255 

36 

98613 

•01406 

24 

6 

96907 

1-03192'54 

37 

98671 

•01347 

23 

7 

96963 

1-0313253 

38 

98728 

•01288 

22 

8 

97020 

1-0307252 

39 

98786 

•01229 

21 

9 

97076 

1-03012  51 

40 

98843 

•01170 

20 

10 

97133 

1-02952  50 

41 

98901 

•01112 

19 

11 

97189 

1-0289249 

42 

98958 

•01053 

18 

12 

97246 

1-02832  48 

43 

99016 

•00994 

17 

13 

97302 

1-02772  47 

44 

99073 

•00935 

16 

t  .      14 

97359 

1-0271?  46 

45 

99131 

•00876 

15 

15 

97416 

1-02653  45 

46 

99189 

1-00818 

14 

16 

97472 

1-02593  44 

47 

99247 

1-00759 

13 

17 

97529 

1-02533  43 

48 

99304 

1-00701 

12 

18 

97586 

1-02474  42 

49 

99362 

•00642 

li 

19 

97643 

1-02414  41 

50 

99420 

•00583 

Id 

20 

97700 

1-02355  40 

51 

99478 

•00525 

9 

21 

97756 

1-02295  39 

52 

99536 

-00467 

a 

22 

97813 

1-02236  38 

53 

99594 

-00408 

7 

23 

97870 

1-02176  37 

54 

99652 

•00350 

6 

24 

97927 

1-02117  36 

55 

99710 

-00291 

5 

25 

97984 

1-02057  35 

56 

99768 

-00233 

4 

26 

98041 

1-01998  34 

57 

99826 

•00175 

3 

27 

98098 

1-01939  33 

58 

99884 

•00116 

2 

28 

98155 

1-01879  32 

5& 

99942 

-00058 

1 

29 

98213 

1-01820  31 

60 

10000 

•00000 

30 

98270 

1-01761  30 

W 

N.  Cot 

N.  Tan.   M 

"M" 

N.  Cot 

N.Tan. 

~M 

45  Degrees. 

45  Degrees*. 

14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

LOAN  DEPT. 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


LD  21A-60m-3,'65 
(F2336slO)476B 


General  Library 
University  of  Calif c 
Berkeley 


W3O6235 

TA 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


